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Answer :
Let's solve the equation step-by-step and identify which process is not part of the solution:
The original equation is:
[tex]\[ 4(3x - 6) = 24 \][/tex]
Step 1: Distribute
- We use the distributive property.
- Distribute the 4 into the parentheses:
[tex]\[ 4 \times 3x - 4 \times 6 = 12x - 24 \][/tex]
- Now, the equation is:
[tex]\[ 12x - 24 = 24 \][/tex]
Step 2: Add to both sides
- We add 24 to both sides to isolate the variable term:
[tex]\[ 12x - 24 + 24 = 24 + 24 \][/tex]
- This simplifies to:
[tex]\[ 12x = 48 \][/tex]
Step 3: Divide to solve for [tex]\( x \)[/tex]
- To solve for [tex]\( x \)[/tex], divide both sides by 12:
[tex]\[ \frac{12x}{12} = \frac{48}{12} \][/tex]
- This gives:
[tex]\[ x = 4 \][/tex]
Now, let's review the choices:
A. Using the distributive property - Yes, this was used in Step 1.
B. Simplifying by combining variable terms - This is not explicitly part of the solution process. We didn't have multiple variable terms to combine.
C. Dividing both sides by 12 to isolate the variable - Yes, this was used in Step 3.
D. Adding 24 to both sides to isolate the variable term - Yes, this was used in Step 2.
The process that was not part of the solution is:
B. Simplifying by combining variable terms.
The original equation is:
[tex]\[ 4(3x - 6) = 24 \][/tex]
Step 1: Distribute
- We use the distributive property.
- Distribute the 4 into the parentheses:
[tex]\[ 4 \times 3x - 4 \times 6 = 12x - 24 \][/tex]
- Now, the equation is:
[tex]\[ 12x - 24 = 24 \][/tex]
Step 2: Add to both sides
- We add 24 to both sides to isolate the variable term:
[tex]\[ 12x - 24 + 24 = 24 + 24 \][/tex]
- This simplifies to:
[tex]\[ 12x = 48 \][/tex]
Step 3: Divide to solve for [tex]\( x \)[/tex]
- To solve for [tex]\( x \)[/tex], divide both sides by 12:
[tex]\[ \frac{12x}{12} = \frac{48}{12} \][/tex]
- This gives:
[tex]\[ x = 4 \][/tex]
Now, let's review the choices:
A. Using the distributive property - Yes, this was used in Step 1.
B. Simplifying by combining variable terms - This is not explicitly part of the solution process. We didn't have multiple variable terms to combine.
C. Dividing both sides by 12 to isolate the variable - Yes, this was used in Step 3.
D. Adding 24 to both sides to isolate the variable term - Yes, this was used in Step 2.
The process that was not part of the solution is:
B. Simplifying by combining variable terms.
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