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Answer :
Let's solve the equation step-by-step and identify which part is not part of the solution process from the provided options:
Original equation:
[tex]\[ 4(3x - 6) = 24 \][/tex]
Step 1: Use the distributive property
To simplify the left side of the equation, we distribute the 4:
[tex]\[ 4 \cdot 3x - 4 \cdot 6 = 24 \][/tex]
[tex]\[ 12x - 24 = 24 \][/tex]
Step 2: Add 24 to both sides to isolate the variable term
To move the constant term from the left side, we add 24 to both sides:
[tex]\[ 12x - 24 + 24 = 24 + 24 \][/tex]
[tex]\[ 12x = 48 \][/tex]
Step 3: Divide both sides by 12 to isolate the variable
To solve for [tex]\( x \)[/tex], we divide both sides by 12:
[tex]\[ \frac{12x}{12} = \frac{48}{12} \][/tex]
[tex]\[ x = 4 \][/tex]
Now, let's analyze the given multiple-choice options:
A. Simplifying by combining variable terms
- This would apply if we had more than one term involving [tex]\( x \)[/tex], which we do not in our steps. There was no need to combine variable terms, as we only had one term involving [tex]\( x \)[/tex].
B. Using the distributive property
- Yes, we used the distributive property in the first step.
C. Adding 24 to both sides to isolate the variable term
- Yes, we added 24 to both sides in the second step to isolate the variable term.
D. Dividing both sides by 12 to isolate the variable
- Yes, we divided both sides by 12 in the final step to solve for [tex]\( x \)[/tex].
From the steps, it's clear that A. Simplifying by combining variable terms is not part of the solution process for this particular equation since there was no instance where we combined variable terms.
Thus, the answer is:
A. Simplifying by combining variable terms
Original equation:
[tex]\[ 4(3x - 6) = 24 \][/tex]
Step 1: Use the distributive property
To simplify the left side of the equation, we distribute the 4:
[tex]\[ 4 \cdot 3x - 4 \cdot 6 = 24 \][/tex]
[tex]\[ 12x - 24 = 24 \][/tex]
Step 2: Add 24 to both sides to isolate the variable term
To move the constant term from the left side, we add 24 to both sides:
[tex]\[ 12x - 24 + 24 = 24 + 24 \][/tex]
[tex]\[ 12x = 48 \][/tex]
Step 3: Divide both sides by 12 to isolate the variable
To solve for [tex]\( x \)[/tex], we divide both sides by 12:
[tex]\[ \frac{12x}{12} = \frac{48}{12} \][/tex]
[tex]\[ x = 4 \][/tex]
Now, let's analyze the given multiple-choice options:
A. Simplifying by combining variable terms
- This would apply if we had more than one term involving [tex]\( x \)[/tex], which we do not in our steps. There was no need to combine variable terms, as we only had one term involving [tex]\( x \)[/tex].
B. Using the distributive property
- Yes, we used the distributive property in the first step.
C. Adding 24 to both sides to isolate the variable term
- Yes, we added 24 to both sides in the second step to isolate the variable term.
D. Dividing both sides by 12 to isolate the variable
- Yes, we divided both sides by 12 in the final step to solve for [tex]\( x \)[/tex].
From the steps, it's clear that A. Simplifying by combining variable terms is not part of the solution process for this particular equation since there was no instance where we combined variable terms.
Thus, the answer is:
A. Simplifying by combining variable terms
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