High School

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

Answer :

To solve the equation [tex]\(4(3x - 6) = 24\)[/tex], let's analyze each step provided and see which option is not part of the solution process.

1. Step 1: Using the Distributive Property
- We start by distributing the 4 into the terms inside the parentheses in the original equation [tex]\(4(3x - 6)\)[/tex].
- This gives: [tex]\(12x - 24 = 24\)[/tex].

2. Step 2: Adding to Isolate the Variable Term
- Next, we add 24 to both sides of the equation to get rid of the [tex]\(-24\)[/tex] on the left side.
- It becomes: [tex]\(12x - 24 + 24 = 24 + 24\)[/tex], which simplifies to [tex]\(12x = 48\)[/tex].

3. Step 3: Dividing to Isolate the Variable
- Lastly, we divide both sides by 12 to solve for [tex]\(x\)[/tex].
- [tex]\( \frac{12x}{12} = \frac{48}{12} \)[/tex] results in [tex]\(x = 4\)[/tex].

Given these steps, let's match them with the choices:

A. Simplifying by combining variable terms - This involves combining terms that have the same variable, but our equation never had more than one [tex]\(x\)[/tex]-term to combine. This is not part of the solution steps we used.

B. Using the distributive property - This was used in Step 1 when expanding [tex]\(4(3x - 6)\)[/tex] to [tex]\(12x - 24\)[/tex].

C. Dividing both sides by 12 to isolate the variable - This was done in Step 4 to solve for [tex]\(x\)[/tex].

D. Adding 24 to both sides to isolate the variable term - This was done in Step 2 to move the constant term from one side to the other.

The step that is not part of the solution process is:
A. Simplifying by combining variable terms.