Which Equations Have The Same Value Of $x$ As 5 6 X + 2 3 = − 9 \frac{5}{6} X+\frac{2}{3}=-9 6 5 X + 3 2 = − 9 ? Select Three Options.A. 6 ( 5 6 X + 2 3 ) = − 9 6\left(\frac{5}{6} X+\frac{2}{3}\right)=-9 6 ( 6 5 X + 3 2 ) = − 9 B. 6 ( 5 6 X + 2 3 ) = − 9 ( 6 6\left(\frac{5}{6} X+\frac{2}{3}\right)=-9(6 6 ( 6 5 X + 3 2 ) = − 9 ( 6 ]C. $5

Mar 11, 2025 by ADMIN 353 views

**Solving Linear Equations: A Step-by-Step Guide**

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will explore the process of solving linear equations, with a focus on the equation $\frac{5}{6} x+\frac{2}{3}=-9$ . We will also examine three options that have the same value of $x$ as the given equation and determine which ones are correct.

Understanding Linear Equations

A linear equation is an equation in which the highest power of the variable (in this case, $x$ ) is 1. The general form of a linear equation is:

ax + b = c

where $a$ , $b$ , and $c$ are constants, and $x$ is the variable.

Solving the Given Equation

The given equation is:

\frac{5}{6} x+\frac{2}{3}=-9

To solve for $x$ , we need to isolate the variable on one side of the equation. We can start by getting rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 6.

from fractions import Fraction
equation = Fraction(5, 6) * x + Fraction(2, 3) + 9

equation = 6 * equation

This gives us:

5x + 4 = -54

Next, we can subtract 4 from both sides of the equation to get:

5x = -58

Finally, we can divide both sides of the equation by 5 to solve for $x$ :

x = -\frac{58}{5}

Evaluating the Options

Now that we have solved the given equation, let's examine the three options:

A. $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9$

B. $6\left(\frac{5}{6} x+\frac{2}{3}\right)=-9(6)$

C. $5x + 4 = -54$

Option A is incorrect because it is the original equation multiplied by 6, but it does not have the same value of $x$ as the given equation.

Option B is also incorrect because it is the original equation multiplied by 6, but it has an extra term $-9(6)$ that is not present in the given equation.

Option C is correct because it is the equation we derived by solving the given equation.

Conclusion

In conclusion, solving linear equations requires a step-by-step approach, and it is essential to isolate the variable on one side of the equation. We have demonstrated how to solve the equation $\frac{5}{6} x+\frac{2}{3}=-9$ and evaluated three options to determine which ones have the same value of $x$ as the given equation. By following the steps outlined in this article, students can develop a deeper understanding of linear equations and improve their problem-solving skills.

Additional Resources

For further practice and review, students can try solving other linear equations and exploring different types of equations, such as quadratic equations and systems of equations.

Final Answer

The final answer is:

Option C: $5x + 4 = -54$
Solving Linear Equations: A Q&A Guide =====================================

Introduction

In our previous article, we explored the process of solving linear equations, with a focus on the equation $\frac{5}{6} x+\frac{2}{3}=-9$ . We also examined three options that have the same value of $x$ as the given equation and determined which ones are correct. In this article, we will provide a Q&A guide to help students better understand linear equations and improve their problem-solving skills.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$ ) is 1. The general form of a linear equation is:

ax + b = c

where $a$ , $b$ , and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division. For example, to solve the equation $2x + 3 = 7$ , you can subtract 3 from both sides to get:

2x = 4

Then, you can divide both sides by 2 to solve for $x$ :

x = 2

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation, while the equation $2x + 3 = 7$ is a linear equation.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you can combine like terms and eliminate any fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. For example, to simplify the equation $\frac{1}{2}x + \frac{1}{3}x = 2$ , you can multiply both sides by 6 to get:

3x + 2x = 12

Then, you can combine like terms to get:

5x = 12

Q: What is the order of operations for solving linear equations?

A: The order of operations for solving linear equations is:

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

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you can plug the value of the variable back into the original equation and see if it is true. For example, if you solve the equation $2x + 3 = 7$ and get $x = 2$ , you can plug $x = 2$ back into the original equation to get:

2(2) + 3 = 7

4 + 3 = 7

7 = 7

Since the equation is true, you know that your solution is correct.