College

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

Answer :

Let's analyze the steps provided to solve the equation [tex]\(4(3x - 6) = 24\)[/tex]:

Step 1:
[tex]\[
4(3x - 6) = 24
\][/tex]
- Here, the equation is in its original form.

Step 2:
[tex]\[
12x - 24 = 24
\][/tex]
- This step involves using the distributive property to expand [tex]\(4(3x - 6)\)[/tex] into [tex]\(12x - 24\)[/tex].

Step 3:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
- This step involves adding 24 to both sides of the equation to eliminate the constant term on the left side.

Step 4:
[tex]\[
12x = 48
\][/tex]
- Simplifying the equation after adding 24 to both sides.

Step 5:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
- Here, we divide both sides by 12 to isolate the variable [tex]\(x\)[/tex].

Step 6:
[tex]\[
x = 4
\][/tex]
- Solving for [tex]\(x\)[/tex].

Let's determine which of the given options are part of the solution process:

A. Using the distributive property:
- This is clearly part of the solution process in Step 2.

B. Dividing both sides by 12 to isolate the variable:
- This happens in Step 5.

C. Adding 24 to both sides to isolate the variable term:
- This is done in Step 3.

D. Simplifying by combining variable terms:
- We do not see any step combining variable terms. All the steps involve simplifying or isolating terms.

Therefore, the step that is NOT part of the solution process is:
D. Simplifying by combining variable terms