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Answer :
To solve the equation [tex]\(4(3x - 6) = 24\)[/tex], let's follow the steps one-by-one and analyze them:
1. Original Equation:
[tex]\[
4(3x - 6) = 24
\][/tex]
2. Step 1: Using the Distributive Property
Distribute the 4 into the parentheses:
[tex]\[
4 \cdot 3x - 4 \cdot 6 = 24
\][/tex]
Simplify:
[tex]\[
12x - 24 = 24
\][/tex]
3. Step 2: Adding 24 to Both Sides to Isolate the Variable Term
Add 24 to both sides to move the constant term:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
Simplify:
[tex]\[
12x = 48
\][/tex]
4. Step 3: Dividing Both Sides by 12 to Isolate the Variable
Divide both sides by 12:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
Simplify:
[tex]\[
x = 4
\][/tex]
From the analysis above, we can see the specific steps that are 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
However, the step "Simplifying by combining variable terms" is not part of the solution process because there are no multiple variable terms to combine in the given steps.
Thus, the answer is:
D. Simplifying by combining variable terms
1. Original Equation:
[tex]\[
4(3x - 6) = 24
\][/tex]
2. Step 1: Using the Distributive Property
Distribute the 4 into the parentheses:
[tex]\[
4 \cdot 3x - 4 \cdot 6 = 24
\][/tex]
Simplify:
[tex]\[
12x - 24 = 24
\][/tex]
3. Step 2: Adding 24 to Both Sides to Isolate the Variable Term
Add 24 to both sides to move the constant term:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
Simplify:
[tex]\[
12x = 48
\][/tex]
4. Step 3: Dividing Both Sides by 12 to Isolate the Variable
Divide both sides by 12:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
Simplify:
[tex]\[
x = 4
\][/tex]
From the analysis above, we can see the specific steps that are 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
However, the step "Simplifying by combining variable terms" is not part of the solution process because there are no multiple variable terms to combine in the given steps.
Thus, the answer is:
D. Simplifying by combining variable terms
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