Solve The Equation For X X X . 27 ( X − 108 ) = 54 27(x - 108) = 54 27 ( X − 108 ) = 54 A. 106 B. 54 C. 108 D. 110Please Select The Best Answer From The Choices Provided:A, B, C, Or D.

Mar 9, 2025 by ADMIN 188 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 focus on solving a specific linear equation, $27(x - 108) = 54$ , and provide a step-by-step guide on how to arrive at the solution.

Understanding the Equation

The given equation is $27(x - 108) = 54$ . To solve for $x$ , we need to isolate the variable $x$ on one side of the equation. The equation involves a linear expression inside the parentheses, which we need to simplify and then solve for $x$ .

Step 1: Distribute the Coefficient

The first step in solving the equation is to distribute the coefficient $27$ to the terms inside the parentheses. This means multiplying $27$ by each term inside the parentheses.

27(x - 108) = 27x - 2916

Step 2: Simplify the Equation

Now that we have distributed the coefficient, we can simplify the equation by combining like terms.

27x - 2916 = 54

Step 3: Add 2916 to Both Sides

To isolate the term with the variable $x$ , we need to add $2916$ to both sides of the equation. This will eliminate the negative term and allow us to solve for $x$ .

27x = 54 + 2916

Step 4: Simplify the Right Side

Now that we have added $2916$ to both sides, we can simplify the right side of the equation.

27x = 2970

Step 5: Divide Both Sides by 27

To solve for $x$ , we need to divide both sides of the equation by $27$ . This will isolate the variable $x$ and give us the solution.

x = 2970 / 27

Step 6: Simplify the Fraction

Now that we have divided both sides by $27$ , we can simplify the fraction to find the value of $x$ .

x = 110

Conclusion

In this article, we have solved the linear equation $27(x - 108) = 54$ using a step-by-step approach. We distributed the coefficient, simplified the equation, added $2916$ to both sides, simplified the right side, divided both sides by $27$ , and finally simplified the fraction to find the value of $x$ . The solution to the equation is $x = 110$ .

Answer

The correct answer is:

A. 106: Incorrect
B. 54: Incorrect
C. 108: Incorrect
D. 110: Correct

Discussion

Introduction

In our previous article, we solved the linear equation $27(x - 108) = 54$ using a step-by-step approach. In this article, we will provide a Q&A guide to help students understand the concepts and techniques involved in solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. In other words, it is an equation that can be written in the form $ax + b = c$ , where $a$ , $b$ , and $c$ are constants.

Q: What are the steps involved in solving a linear equation?

A: The steps involved in solving a linear equation are:

Distribute the coefficient to the terms inside the parentheses.
Simplify the equation by combining like terms.
Add or subtract the same value to both sides of the equation.
Multiply or divide both sides of the equation by the same value.
Simplify the resulting expression to find the value of the variable.

Q: How do I distribute the coefficient to the terms inside the parentheses?

A: To distribute the coefficient, you need to multiply the coefficient by each term inside the parentheses. For example, if you have the equation $3(x + 2)$ , you would distribute the coefficient 3 to the terms inside the parentheses as follows:

$3(x + 2) = 3x + 6$

Q: What is the difference between adding and subtracting the same value to both sides of the equation?

A: Adding the same value to both sides of the equation is equivalent to subtracting the same value from both sides of the equation. For example, if you have the equation $x + 3 = 5$ , you can add 3 to both sides of the equation to get:

$x + 3 + 3 = 5 + 3$

$x + 6 = 8$

Or, you can subtract 3 from both sides of the equation to get:

$x + 3 - 3 = 5 - 3$

$x = 2$

Q: How do I simplify the resulting expression to find the value of the variable?

A: To simplify the resulting expression, you need to combine like terms and perform any necessary arithmetic operations. For example, if you have the equation $x + 2x = 5$ , you would combine the like terms as follows:

$3x = 5$

$x = 5/3$

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

Not distributing the coefficient to the terms inside the parentheses.
Not simplifying the equation by combining like terms.
Not adding or subtracting the same value to both sides of the equation.
Not multiplying or dividing both sides of the equation by the same value.
Not simplifying the resulting expression to find the value of the variable.

Conclusion

In this article, we have provided a Q&A guide to help students understand the concepts and techniques involved in solving linear equations. We have covered topics such as the definition of a linear equation, the steps involved in solving a linear equation, and common mistakes to avoid. By following these steps and avoiding these common mistakes, students can become proficient in solving linear equations and apply this skill to a wide range of mathematical problems.

Answer

The correct answers to the Q&A guide are:

Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.
Q: What are the steps involved in solving a linear equation? A: The steps involved in solving a linear equation are: 1. Distribute the coefficient to the terms inside the parentheses. 2. Simplify the equation by combining like terms. 3. Add or subtract the same value to both sides of the equation. 4. Multiply or divide both sides of the equation by the same value. 5. Simplify the resulting expression to find the value of the variable.
Q: How do I distribute the coefficient to the terms inside the parentheses? A: To distribute the coefficient, you need to multiply the coefficient by each term inside the parentheses.
Q: What is the difference between adding and subtracting the same value to both sides of the equation? A: Adding the same value to both sides of the equation is equivalent to subtracting the same value from both sides of the equation.
Q: How do I simplify the resulting expression to find the value of the variable? A: To simplify the resulting expression, you need to combine like terms and perform any necessary arithmetic operations.
Q: What are some common mistakes to avoid when solving linear equations? A: Some common mistakes to avoid when solving linear equations include: not distributing the coefficient to the terms inside the parentheses, not simplifying the equation by combining like terms, not adding or subtracting the same value to both sides of the equation, not multiplying or dividing both sides of the equation by the same value, and not simplifying the resulting expression to find the value of the variable.