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Answer :
To solve the equation [tex]\(4(3x - 6) = 24\)[/tex], let's analyze each step provided and see which option is not part of the solution process.
1. Step 1: Using the Distributive Property
- We start by distributing the 4 into the terms inside the parentheses in the original equation [tex]\(4(3x - 6)\)[/tex].
- This gives: [tex]\(12x - 24 = 24\)[/tex].
2. Step 2: Adding to Isolate the Variable Term
- Next, we add 24 to both sides of the equation to get rid of the [tex]\(-24\)[/tex] on the left side.
- It becomes: [tex]\(12x - 24 + 24 = 24 + 24\)[/tex], which simplifies to [tex]\(12x = 48\)[/tex].
3. Step 3: Dividing to Isolate the Variable
- Lastly, we divide both sides by 12 to solve for [tex]\(x\)[/tex].
- [tex]\( \frac{12x}{12} = \frac{48}{12} \)[/tex] results in [tex]\(x = 4\)[/tex].
Given these steps, let's match them with the choices:
A. Simplifying by combining variable terms - This involves combining terms that have the same variable, but our equation never had more than one [tex]\(x\)[/tex]-term to combine. This is not part of the solution steps we used.
B. Using the distributive property - This was used in Step 1 when expanding [tex]\(4(3x - 6)\)[/tex] to [tex]\(12x - 24\)[/tex].
C. Dividing both sides by 12 to isolate the variable - This was done in Step 4 to solve for [tex]\(x\)[/tex].
D. Adding 24 to both sides to isolate the variable term - This was done in Step 2 to move the constant term from one side to the other.
The step that is not part of the solution process is:
A. Simplifying by combining variable terms.
1. Step 1: Using the Distributive Property
- We start by distributing the 4 into the terms inside the parentheses in the original equation [tex]\(4(3x - 6)\)[/tex].
- This gives: [tex]\(12x - 24 = 24\)[/tex].
2. Step 2: Adding to Isolate the Variable Term
- Next, we add 24 to both sides of the equation to get rid of the [tex]\(-24\)[/tex] on the left side.
- It becomes: [tex]\(12x - 24 + 24 = 24 + 24\)[/tex], which simplifies to [tex]\(12x = 48\)[/tex].
3. Step 3: Dividing to Isolate the Variable
- Lastly, we divide both sides by 12 to solve for [tex]\(x\)[/tex].
- [tex]\( \frac{12x}{12} = \frac{48}{12} \)[/tex] results in [tex]\(x = 4\)[/tex].
Given these steps, let's match them with the choices:
A. Simplifying by combining variable terms - This involves combining terms that have the same variable, but our equation never had more than one [tex]\(x\)[/tex]-term to combine. This is not part of the solution steps we used.
B. Using the distributive property - This was used in Step 1 when expanding [tex]\(4(3x - 6)\)[/tex] to [tex]\(12x - 24\)[/tex].
C. Dividing both sides by 12 to isolate the variable - This was done in Step 4 to solve for [tex]\(x\)[/tex].
D. Adding 24 to both sides to isolate the variable term - This was done in Step 2 to move the constant term from one side to the other.
The step that is not part of the solution process is:
A. Simplifying by combining variable terms.
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