When $x=5$, The Value Of The Expression 20 − 25 + X − 2 ( X − 10 \frac{20}{-25+x}-2(x-10 − 25 + X 20 − 2 ( X − 10 ] Is:A. -21 B. -9 C. 9 D. 19

Mar 13, 2025 by ADMIN 150 views

$When $x=5$, the value of the expression $\frac{20}{-25+x}-2(x-10)$ is:$

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Introduction

Understanding the Problem

The given problem involves evaluating an algebraic expression when a specific value is assigned to the variable $x$ . We are required to find the value of the expression $\frac{20}{-25+x}-2(x-10)$ when $x=5$ . This problem requires us to substitute the given value of $x$ into the expression and simplify it to obtain the final result.

Step 1: Substitute the value of $x$ into the expression

Substitution

To evaluate the expression, we need to substitute $x=5$ into the given expression. This involves replacing every occurrence of $x$ with $5$ in the expression.

Step 2: Simplify the expression

Simplification

After substituting $x=5$ into the expression, we get $\frac{20}{-25+5}-2(5-10)$ . Now, we need to simplify this expression by performing the arithmetic operations.

Step 3: Evaluate the expression

Evaluation

To simplify the expression, we need to follow the order of operations (PEMDAS):

Evaluate the expression inside the parentheses: $-25+5 = -20$ and $5-10 = -5$ .
Substitute the values back into the expression: $\frac{20}{-20}-2(-5)$ .
Simplify the expression: $-1+10$ .

Step 4: Calculate the final result

Final Result

Now, we need to calculate the final result by adding the two numbers: $-1+10 = 9$ .

Conclusion

Final Answer

Therefore, the value of the expression $\frac{20}{-25+x}-2(x-10)$ when $x=5$ is $\boxed{9}$ .

Why is this the correct answer?

Explanation

The correct answer is obtained by following the order of operations and simplifying the expression. The expression involves evaluating a fraction and subtracting a product, which requires careful application of the rules of arithmetic.

What are the key concepts involved in this problem?

Key Concepts

The key concepts involved in this problem are:

Substitution: Replacing variables with specific values in an expression.
Simplification: Combining like terms and performing arithmetic operations to simplify an expression.
Order of operations (PEMDAS): Following a specific order to evaluate expressions involving multiple operations.

How can this problem be applied in real-life situations?

Real-Life Applications

This problem can be applied in real-life situations where algebraic expressions need to be evaluated and simplified. For example, in physics, algebraic expressions are used to describe the motion of objects, and in economics, algebraic expressions are used to model economic systems.

What are the common mistakes that students make when solving this problem?

Common Mistakes

Common mistakes that students make when solving this problem include:

Failing to substitute the value of $x$ into the expression.
Not following the order of operations (PEMDAS).
Not simplifying the expression correctly.

How can students avoid these mistakes?

Tips for Students

To avoid these mistakes, students should:

Carefully read and understand the problem.
Substitute the value of $x$ into the expression correctly.
Follow the order of operations (PEMDAS) carefully.
Simplify the expression correctly.

What are the benefits of solving this problem?

Benefits

Solving this problem has several benefits, including:

Developing algebraic skills and techniques.
Improving problem-solving skills and critical thinking.
Building confidence in solving mathematical problems.

What are the limitations of this problem?

Limitations

The limitations of this problem include:

It is a relatively simple problem and may not challenge advanced students.
It may not be relevant to real-life situations for some students.

What are the future directions for this problem?

Future Directions

Future directions for this problem include:

Developing more complex algebraic expressions and evaluating them.
Applying algebraic techniques to real-life situations.
Exploring the connections between algebra and other branches of mathematics.

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Q: What is the value of the expression $\frac{20}{-25+x}-2(x-10)$ when $x=5$ ?

A: The value of the expression $\frac{20}{-25+x}-2(x-10)$ when $x=5$ is $\boxed{9}$ .

Q: How do I substitute the value of $x$ into the expression?

A: To substitute the value of $x$ into the expression, replace every occurrence of $x$ with the given value, which is $5$ in this case.

Q: What is the order of operations (PEMDAS) and how do I apply it to this problem?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

In this problem, we need to follow the order of operations to simplify the expression.

Q: How do I simplify the expression $\frac{20}{-20}-2(-5)$ ?

A: To simplify the expression, we need to follow the order of operations. First, we evaluate the expression inside the parentheses: $-20$ and $-5$ . Then, we substitute the values back into the expression: $\frac{20}{-20}-2(-5)$ . Finally, we simplify the expression by performing the arithmetic operations: $-1+10$ .

Q: What are some common mistakes that students make when solving this problem?

A: Some common mistakes that students make when solving this problem include:

Failing to substitute the value of $x$ into the expression.
Not following the order of operations (PEMDAS).
Not simplifying the expression correctly.

Q: How can I avoid these mistakes?

A: To avoid these mistakes, you should:

Carefully read and understand the problem.
Substitute the value of $x$ into the expression correctly.
Follow the order of operations (PEMDAS) carefully.
Simplify the expression correctly.

Q: What are the benefits of solving this problem?

A: Solving this problem has several benefits, including:

Developing algebraic skills and techniques.
Improving problem-solving skills and critical thinking.
Building confidence in solving mathematical problems.

Q: What are the limitations of this problem?

A: The limitations of this problem include:

It is a relatively simple problem and may not challenge advanced students.
It may not be relevant to real-life situations for some students.

Q: What are the future directions for this problem?

A: Future directions for this problem include:

Developing more complex algebraic expressions and evaluating them.
Applying algebraic techniques to real-life situations.
Exploring the connections between algebra and other branches of mathematics.

Q: Can I apply the concepts learned from this problem to other areas of mathematics?

A: Yes, the concepts learned from this problem can be applied to other areas of mathematics, such as:

Solving systems of linear equations.
Graphing functions.
Analyzing and solving quadratic equations.

Q: How can I practice and improve my skills in solving algebraic expressions?

A: To practice and improve your skills in solving algebraic expressions, you can:

Practice solving different types of algebraic expressions.
Use online resources and practice problems to help you improve your skills.
Seek help from a teacher or tutor if you need additional support.

Q: What are some real-life applications of algebraic expressions?

A: Algebraic expressions have many real-life applications, including:

Modeling population growth and decline.
Analyzing and solving financial problems.
Designing and optimizing systems.

Q: Can I use algebraic expressions to solve real-world problems?

A: Yes, algebraic expressions can be used to solve real-world problems. By applying algebraic techniques and concepts, you can model and analyze complex systems and make informed decisions.