College

2.6.3 Test (CST): Solving Equations and Inequalities

Steps for solving [tex]$4(3x - 6) = 24$[/tex] are shown.

[tex]
\[
\begin{aligned}
4(3x - 6) & = 24 & & \text{Original Equation} \\
12x - 24 & = 24 & & \text{Step 1} \\
12x - 24 + 24 & = 24 + 24 & & \text{Step 2} \\
12x & = 48 & & \text{Step 3} \\
\frac{12x}{12} & = \frac{48}{12} & & \text{Step 4} \\
x & = 4 & & \text{Step 5}
\end{aligned}
\]
[/tex]

Which of these is not part of the solution process?

A. Dividing both sides by 12 to isolate the variable
B. Adding 24 to both sides to isolate the variable term
C. Using the distributive property
D. Simplifying by combining variable terms

Answer :

To determine which step is not part of the solution process for solving the equation [tex]\(4(3x - 6) = 24\)[/tex], let's go through the steps presented:

1. Original Equation: [tex]\(4(3x - 6) = 24\)[/tex]

2. Step 1 - Distributive Property:
[tex]\[
4(3x - 6) = 12x - 24
\][/tex]
This step involves using the distributive property to multiply 4 by both terms inside the parentheses.

3. Step 2 - Adding 24 to Both Sides:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
The purpose is to eliminate the [tex]\(-24\)[/tex] by adding 24 to both sides, resulting in:
[tex]\[
12x = 48
\][/tex]

4. Step 4 - Dividing by 12:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
This step is used to isolate the variable [tex]\(x\)[/tex], resulting in:
[tex]\[
x = 4
\][/tex]

By examining these steps, we can identify which choice does not fit:

- Choice A: Dividing both sides by 12 to isolate the variable. This is done in Step 4.
- Choice B: Adding 24 to both sides to isolate the variable term. This is done in Step 2.
- Choice C: Using the distributive property. This is done in Step 1.
- Choice D: Simplifying by combining variable terms. This involves combining terms like [tex]\(3x\)[/tex] or similar, which does not happen in this solution process because there are no other [tex]\(x\)[/tex] terms to combine.

Therefore, the choice that is not part of the solution process is:

D. Simplifying by combining variable terms, as this process did not take place in the solution provided.