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

Answer :

To solve the equation [tex]\(4(3x - 6) = 24\)[/tex], let's go through the steps shown:

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

2. Distributive Property (Step 1):
We apply the distributive property to eliminate the parentheses:
[tex]\(4 \cdot (3x) - 4 \cdot 6 = 24\)[/tex],
which simplifies to [tex]\(12x - 24 = 24\)[/tex].

3. Adding to Both Sides (Step 2):
To isolate the variable term [tex]\(12x\)[/tex], we add 24 to both sides:
[tex]\(12x - 24 + 24 = 24 + 24\)[/tex],
which simplifies to [tex]\(12x = 48\)[/tex].

4. Dividing (Step 4):
To solve for [tex]\(x\)[/tex], we divide both sides by 12:
[tex]\(\frac{12x}{12} = \frac{48}{12}\)[/tex],
which simplifies to [tex]\(x = 4\)[/tex].

5. Solution (Step 5):
We find that [tex]\(x = 4\)[/tex].

Looking at the options to determine which step is not part of the solution process:

A. Simplifying by combining variable terms - This is not applicable here, as there is only one term involving [tex]\(x\)[/tex].

B. Dividing both sides by 12 to isolate the variable - This does happen in Step 4.

C. Adding 24 to both sides to isolate the variable term - This happens in Step 2.

D. Using the distributive property - This occurs in Step 1.

Therefore, the step not part of the solution process is A. Simplifying by combining variable terms.