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. Dividing both sides by 12 to isolate the variable
B. Using the distributive property

Answer :

To solve the equation [tex]\( 4(3x - 6) = 24 \)[/tex], we need to identify each step in the process and determine which option is not part of the solution process. Let's break down the steps:

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

2. Step 1 - Using the Distributive Property:
- We distribute 4 into the terms inside the parentheses: [tex]\( 4 \times 3x \)[/tex] and [tex]\( 4 \times -6 \)[/tex].
- This gives us: [tex]\( 12x - 24 = 24 \)[/tex].
- This step involves the use of the distributive property.

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

4. Step 3 - Dividing Both Sides by 12:
- We divide both sides of the equation by 12 to solve for [tex]\( x \)[/tex]: [tex]\( \frac{12x}{12} = \frac{48}{12} \)[/tex].
- This gives us: [tex]\( x = 4 \)[/tex].

Now let's evaluate the options given:

- Option A: Dividing both sides by 12 to isolate the variable.
- This step is part of the solution process as seen in Step 3.

- Option B: Using the distributive property.
- This step is used in Step 1, where we distributed the 4 to the terms inside the parentheses.

Therefore, both steps, A and B, are part of the solution process, and none of these steps are incorrectly listed as not being part of the process.

In conclusion, both Options A and B are indeed part of the solution, and the question seems to suggest an option not fitting, but in reality, all listed processes are valid steps in solving the equation.