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Answer :
Let's analyze the steps shown for solving the equation [tex]\(4(3x-6) = 24\)[/tex] to determine which option is not part of the solution process. Here are the steps explained:
1. Original Equation: [tex]\(4(3x-6) = 24\)[/tex]
- This is the equation we start with.
2. Step 1: [tex]\(12x - 24 = 24\)[/tex]
- Here, the distributive property is used. The expression [tex]\(4(3x-6)\)[/tex] is expanded to [tex]\(12x - 24\)[/tex].
3. Step 2: [tex]\(12x - 24 + 24 = 24 + 24\)[/tex]
- [tex]\(24\)[/tex] is added to both sides to isolate the variable term. This step is about eliminating the constant on the left side by adding [tex]\(24\)[/tex].
4. Step 3: [tex]\(12x = 48\)[/tex]
- After adding [tex]\(24\)[/tex] to both sides, the equation simplifies to this form.
5. Step 4: [tex]\(\frac{12x}{12} = \frac{48}{12}\)[/tex]
- Both sides are divided by [tex]\(12\)[/tex] to solve for [tex]\(x\)[/tex].
6. Step 5: [tex]\(x = 4\)[/tex]
- This is the final solution for the value of [tex]\(x\)[/tex].
Now, review the options:
A. Adding 24 to both sides to isolate the variable term: This is part of Step 2.
B. Simplifying by combining variable terms: There is no step where variable terms are combined, as there is only one variable term, [tex]\(12x\)[/tex].
C. Dividing both sides by 12 to isolate the variable: This is part of Step 4.
D. Using the distributive property: This occurs in Step 1.
The option that is not part of the solution process is B. Simplifying by combining variable terms. This does not occur in the given steps because there are no multiple variable terms that need to be combined.
1. Original Equation: [tex]\(4(3x-6) = 24\)[/tex]
- This is the equation we start with.
2. Step 1: [tex]\(12x - 24 = 24\)[/tex]
- Here, the distributive property is used. The expression [tex]\(4(3x-6)\)[/tex] is expanded to [tex]\(12x - 24\)[/tex].
3. Step 2: [tex]\(12x - 24 + 24 = 24 + 24\)[/tex]
- [tex]\(24\)[/tex] is added to both sides to isolate the variable term. This step is about eliminating the constant on the left side by adding [tex]\(24\)[/tex].
4. Step 3: [tex]\(12x = 48\)[/tex]
- After adding [tex]\(24\)[/tex] to both sides, the equation simplifies to this form.
5. Step 4: [tex]\(\frac{12x}{12} = \frac{48}{12}\)[/tex]
- Both sides are divided by [tex]\(12\)[/tex] to solve for [tex]\(x\)[/tex].
6. Step 5: [tex]\(x = 4\)[/tex]
- This is the final solution for the value of [tex]\(x\)[/tex].
Now, review the options:
A. Adding 24 to both sides to isolate the variable term: This is part of Step 2.
B. Simplifying by combining variable terms: There is no step where variable terms are combined, as there is only one variable term, [tex]\(12x\)[/tex].
C. Dividing both sides by 12 to isolate the variable: This is part of Step 4.
D. Using the distributive property: This occurs in Step 1.
The option that is not part of the solution process is B. Simplifying by combining variable terms. This does not occur in the given steps because there are no multiple variable terms that need to be combined.
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