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.
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.
