Which Equation Can Be Used To Represent three Minus The Difference Of A Number And One Equals One-half Of The Difference Of Three Times The Same Number And Four?A. 3 − ( 1 − N ) = 1 2 ( 4 − 3 N 3 - (1 - N) = \frac{1}{2}(4 - 3n 3 − ( 1 − N ) = 2 1 ​ ( 4 − 3 N ]B. $3 - (n - 1) = \frac{1}{2}(3n -

by ADMIN 297 views

Understanding the Problem Statement

The given problem statement is a mathematical expression that involves various operations such as subtraction, multiplication, and division. To represent this statement as an equation, we need to carefully analyze the given expression and translate it into a mathematical formula.

The problem statement can be broken down into several key components:

  • "Three minus the difference of a number and one"
  • "equals one-half of the difference of three times the same number and four"

Breaking Down the Problem Statement

Let's start by analyzing the first part of the problem statement: "three minus the difference of a number and one." This can be represented mathematically as:

3−(n−1)3 - (n - 1)

where nn is the unknown number.

Analyzing the Second Part of the Problem Statement

The second part of the problem statement is "one-half of the difference of three times the same number and four." This can be represented mathematically as:

12(3n−4)\frac{1}{2}(3n - 4)

Combining the Two Parts of the Problem Statement

Now that we have analyzed both parts of the problem statement, we can combine them to form a single equation. The equation should be in the form of:

3−(n−1)=12(3n−4)3 - (n - 1) = \frac{1}{2}(3n - 4)

Evaluating the Options

We are given two options to choose from:

A. 3−(1−n)=12(4−3n)3 - (1 - n) = \frac{1}{2}(4 - 3n)

B. 3−(n−1)=12(3n−4)3 - (n - 1) = \frac{1}{2}(3n - 4)

Comparing the Options with the Derived Equation

Let's compare the two options with the derived equation:

Option A: 3−(1−n)=12(4−3n)3 - (1 - n) = \frac{1}{2}(4 - 3n)

This option can be simplified as:

3−1+n=12(4−3n)3 - 1 + n = \frac{1}{2}(4 - 3n)

2+n=12(4−3n)2 + n = \frac{1}{2}(4 - 3n)

4+2n=4−3n4 + 2n = 4 - 3n

5n=05n = 0

n=0n = 0

However, this option does not match the derived equation.

Option B: 3−(n−1)=12(3n−4)3 - (n - 1) = \frac{1}{2}(3n - 4)

This option can be simplified as:

3−n+1=12(3n−4)3 - n + 1 = \frac{1}{2}(3n - 4)

4−n=12(3n−4)4 - n = \frac{1}{2}(3n - 4)

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Conclusion

Based on the analysis, we can conclude that neither of the given options matches the derived equation. However, we can simplify the derived equation to match one of the options.

Simplifying the Derived Equation

Let's simplify the derived equation:

3−(n−1)=12(3n−4)3 - (n - 1) = \frac{1}{2}(3n - 4)

3−n+1=12(3n−4)3 - n + 1 = \frac{1}{2}(3n - 4)

4−n=12(3n−4)4 - n = \frac{1}{2}(3n - 4)

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution

Let's try to simplify the equation by multiplying both sides by 2:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 2

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 3

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 4

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 5

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 6

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 7

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 8

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 9

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 10

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3−(n−1))=2(12(3n−4))2(3 - (n - 1)) = 2(\frac{1}{2}(3n - 4))

6−2n+2=3n−46 - 2n + 2 = 3n - 4

8−2n=3n−48 - 2n = 3n - 4

12=5n12 = 5n

125=n\frac{12}{5} = n

However, this option also does not match the derived equation.

Alternative Solution 11

Let's try to simplify the equation by multiplying both sides by 2 and then rearranging the terms:

2(3 - (n - 1<br/> # Q&A: Which Equation Can Be Used to Represent "Three Minus the Difference of a Number and One Equals One-Half of the Difference of Three Times the Same Number and Four"?

Frequently Asked Questions

Q: What is the problem statement?

A: The problem statement is "three minus the difference of a number and one equals one-half of the difference of three times the same number and four."

Q: How can we represent the problem statement as an equation?

A: We can represent the problem statement as an equation by breaking it down into several key components and translating it into a mathematical formula.

Q: What are the key components of the problem statement?

A: The key components of the problem statement are:

  • "Three minus the difference of a number and one"
  • "equals one-half of the difference of three times the same number and four"

Q: How can we represent the first part of the problem statement mathematically?

A: We can represent the first part of the problem statement mathematically as:

3−(n−1)</span></p><p>where<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotationencoding="application/x−tex">n</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.4306em;"></span><spanclass="mordmathnormal">n</span></span></span></span>istheunknownnumber.</p><h3>Q:Howcanwerepresentthesecondpartoftheproblemstatementmathematically?</h3><p>A:Wecanrepresentthesecondpartoftheproblemstatementmathematicallyas:</p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mostretchy="false">(</mo><mn>3</mn><mi>n</mi><mo>−</mo><mn>4</mn><mostretchy="false">)</mo></mrow><annotationencoding="application/x−tex">12(3n−4)</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:2.0074em;vertical−align:−0.686em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlist−tvlist−t2"><spanclass="vlist−r"><spanclass="vlist"style="height:1.3214em;"><spanstyle="top:−2.314em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="mord"><spanclass="mord">2</span></span></span><spanstyle="top:−3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="frac−line"style="border−bottom−width:0.04em;"></span></span><spanstyle="top:−3.677em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="mord"><spanclass="mord">1</span></span></span></span><spanclass="vlist−s">​</span></span><spanclass="vlist−r"><spanclass="vlist"style="height:0.686em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span><spanclass="mopen">(</span><spanclass="mord">3</span><spanclass="mordmathnormal">n</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">4</span><spanclass="mclose">)</span></span></span></span></span></p><h3>Q:Howcanwecombinethetwopartsoftheproblemstatementtoformasingleequation?</h3><p>A:Wecancombinethetwopartsoftheproblemstatementtoformasingleequationbysettingthemequaltoeachother:</p><pclass=′katex−block′><spanclass="katex−display"><spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"display="block"><semantics><mrow><mn>3</mn><mo>−</mo><mostretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mostretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mostretchy="false">(</mo><mn>3</mn><mi>n</mi><mo>−</mo><mn>4</mn><mostretchy="false">)</mo></mrow><annotationencoding="application/x−tex">3−(n−1)=12(3n−4)</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">3</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mopen">(</span><spanclass="mordmathnormal">n</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">1</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:2.0074em;vertical−align:−0.686em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlist−tvlist−t2"><spanclass="vlist−r"><spanclass="vlist"style="height:1.3214em;"><spanstyle="top:−2.314em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="mord"><spanclass="mord">2</span></span></span><spanstyle="top:−3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="frac−line"style="border−bottom−width:0.04em;"></span></span><spanstyle="top:−3.677em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="mord"><spanclass="mord">1</span></span></span></span><spanclass="vlist−s">​</span></span><spanclass="vlist−r"><spanclass="vlist"style="height:0.686em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span><spanclass="mopen">(</span><spanclass="mord">3</span><spanclass="mordmathnormal">n</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">4</span><spanclass="mclose">)</span></span></span></span></span></p><h3>Q:Whatarethetwooptionsgiventochoosefrom?</h3><p>A:Thetwooptionsgiventochoosefromare:</p><p>A.<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mo>−</mo><mostretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>n</mi><mostretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mostretchy="false">(</mo><mn>4</mn><mo>−</mo><mn>3</mn><mi>n</mi><mostretchy="false">)</mo></mrow><annotationencoding="application/x−tex">3−(1−n)=12(4−3n)</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">3</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mopen">(</span><spanclass="mord">1</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mordmathnormal">n</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:1.1901em;vertical−align:−0.345em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlist−tvlist−t2"><spanclass="vlist−r"><spanclass="vlist"style="height:0.8451em;"><spanstyle="top:−2.655em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">2</span></span></span></span><spanstyle="top:−3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="frac−line"style="border−bottom−width:0.04em;"></span></span><spanstyle="top:−3.394em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">1</span></span></span></span></span><spanclass="vlist−s">​</span></span><spanclass="vlist−r"><spanclass="vlist"style="height:0.345em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span><spanclass="mopen">(</span><spanclass="mord">4</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">3</span><spanclass="mordmathnormal">n</span><spanclass="mclose">)</span></span></span></span></p><p>B.<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mo>−</mo><mostretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mostretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mostretchy="false">(</mo><mn>3</mn><mi>n</mi><mo>−</mo><mn>4</mn><mostretchy="false">)</mo></mrow><annotationencoding="application/x−tex">3−(n−1)=12(3n−4)</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.7278em;vertical−align:−0.0833em;"></span><spanclass="mord">3</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mopen">(</span><spanclass="mordmathnormal">n</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">1</span><spanclass="mclose">)</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:1.1901em;vertical−align:−0.345em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlist−tvlist−t2"><spanclass="vlist−r"><spanclass="vlist"style="height:0.8451em;"><spanstyle="top:−2.655em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">2</span></span></span></span><spanstyle="top:−3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="frac−line"style="border−bottom−width:0.04em;"></span></span><spanstyle="top:−3.394em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">1</span></span></span></span></span><spanclass="vlist−s">​</span></span><spanclass="vlist−r"><spanclass="vlist"style="height:0.345em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span><spanclass="mopen">(</span><spanclass="mord">3</span><spanclass="mordmathnormal">n</span><spanclass="mspace"style="margin−right:0.2222em;"></span><spanclass="mbin">−</span><spanclass="mspace"style="margin−right:0.2222em;"></span></span><spanclass="base"><spanclass="strut"style="height:1em;vertical−align:−0.25em;"></span><spanclass="mord">4</span><spanclass="mclose">)</span></span></span></span></p><h3>Q:Howcanwecomparethetwooptionswiththederivedequation?</h3><p>A:Wecancomparethetwooptionswiththederivedequationbysimplifyingandrearrangingtheterms.</p><h3>Q:Whatistheconclusionbasedontheanalysis?</h3><p>A:Basedontheanalysis,wecanconcludethatneitherofthegivenoptionsmatchesthederivedequation.</p><h3>Q:Howcanwesimplifythederivedequationtomatchoneoftheoptions?</h3><p>A:Wecansimplifythederivedequationbymultiplyingbothsidesby2andthenrearrangingtheterms.</p><h3>Q:Whatisthefinalanswer?</h3><p>A:Unfortunately,thefinalanswerisnotasimplenumber,butratheraconclusionthatneitherofthegivenoptionsmatchesthederivedequation.</p><h2>AdditionalResources</h2><ul><li>Formoreinformationonalgebraicequations,pleaserefertothefollowingresources:<ul><li><ahref="https://www.mathsisfun.com/algebra/equations.html">AlgebraicEquations</a></li><li>[SolvingAlgebraicEquations](<ahref="https://www.khanacademy.org/math/algebra/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7">https://www.khanacademy.org/math/algebra/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7</a></li></ul></li></ul>3 - (n - 1) </span></p> <p>where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> is the unknown number.</p> <h3>Q: How can we represent the second part of the problem statement mathematically?</h3> <p>A: We can represent the second part of the problem statement mathematically as:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo stretchy="false">(</mo><mn>3</mn><mi>n</mi><mo>−</mo><mn>4</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\frac{1}{2}(3n - 4) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mopen">(</span><span class="mord">3</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">4</span><span class="mclose">)</span></span></span></span></span></p> <h3>Q: How can we combine the two parts of the problem statement to form a single equation?</h3> <p>A: We can combine the two parts of the problem statement to form a single equation by setting them equal to each other:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>3</mn><mo>−</mo><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo stretchy="false">(</mo><mn>3</mn><mi>n</mi><mo>−</mo><mn>4</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">3 - (n - 1) = \frac{1}{2}(3n - 4) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mopen">(</span><span class="mord">3</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">4</span><span class="mclose">)</span></span></span></span></span></p> <h3>Q: What are the two options given to choose from?</h3> <p>A: The two options given to choose from are:</p> <p>A. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mo>−</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo stretchy="false">(</mo><mn>4</mn><mo>−</mo><mn>3</mn><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">3 - (1 - n) = \frac{1}{2}(4 - 3n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mopen">(</span><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">3</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span></p> <p>B. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mo>−</mo><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo stretchy="false">(</mo><mn>3</mn><mi>n</mi><mo>−</mo><mn>4</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">3 - (n - 1) = \frac{1}{2}(3n - 4)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mopen">(</span><span class="mord">3</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">4</span><span class="mclose">)</span></span></span></span></p> <h3>Q: How can we compare the two options with the derived equation?</h3> <p>A: We can compare the two options with the derived equation by simplifying and rearranging the terms.</p> <h3>Q: What is the conclusion based on the analysis?</h3> <p>A: Based on the analysis, we can conclude that neither of the given options matches the derived equation.</p> <h3>Q: How can we simplify the derived equation to match one of the options?</h3> <p>A: We can simplify the derived equation by multiplying both sides by 2 and then rearranging the terms.</p> <h3>Q: What is the final answer?</h3> <p>A: Unfortunately, the final answer is not a simple number, but rather a conclusion that neither of the given options matches the derived equation.</p> <h2>Additional Resources</h2> <ul> <li>For more information on algebraic equations, please refer to the following resources: <ul> <li><a href="https://www.mathsisfun.com/algebra/equations.html">Algebraic Equations</a></li> <li>[Solving Algebraic Equations](<a href="https://www.khanacademy.org/math/algebra/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7">https://www.khanacademy.org/math/algebra/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7d7/x2f4f7</a></li> </ul> </li> </ul>