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Answer :
Sure! Let's go through the steps of solving the equation [tex]\(4(3x - 6) = 24\)[/tex] and identify which part is not included in the solution process.
1. Use the Distributive Property:
The equation starts with [tex]\(4(3x - 6)\)[/tex], which means you need to distribute the 4 to both terms inside the parentheses. This leads to:
[tex]\[
12x - 24 = 24
\][/tex]
So, using the distributive property is definitely a step in the process (this relates to choice D).
2. Identify the need for simplifying by combining variable terms:
In the equation [tex]\(12x - 24 = 24\)[/tex], there are no other variable terms to combine. We only have a single variable expression [tex]\(12x\)[/tex]. So, there is no step where you need to combine like terms (this relates to choice B).
3. Add or Subtract to Isolate the Variable Term:
To isolate the term with [tex]\(x\)[/tex], add 24 to both sides of the equation:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
Simplifying the equation gives:
[tex]\[
12x = 48
\][/tex]
Adding 24 to both sides is definitely a valid step in the solution process (this relates to choice C).
4. Divide to Solve for the Variable:
Finally, divide both sides of the equation by 12 to find [tex]\(x\)[/tex]:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
Simplifying gives:
[tex]\[
x = 4
\][/tex]
Dividing both sides by 12 to isolate [tex]\(x\)[/tex] is a crucial step in the process (this relates to choice A).
Given this breakdown, the step that is NOT part of the solution process is:
B. Simplifying by combining variable terms
This is because there was no need to combine variable terms in the given steps.
1. Use the Distributive Property:
The equation starts with [tex]\(4(3x - 6)\)[/tex], which means you need to distribute the 4 to both terms inside the parentheses. This leads to:
[tex]\[
12x - 24 = 24
\][/tex]
So, using the distributive property is definitely a step in the process (this relates to choice D).
2. Identify the need for simplifying by combining variable terms:
In the equation [tex]\(12x - 24 = 24\)[/tex], there are no other variable terms to combine. We only have a single variable expression [tex]\(12x\)[/tex]. So, there is no step where you need to combine like terms (this relates to choice B).
3. Add or Subtract to Isolate the Variable Term:
To isolate the term with [tex]\(x\)[/tex], add 24 to both sides of the equation:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
Simplifying the equation gives:
[tex]\[
12x = 48
\][/tex]
Adding 24 to both sides is definitely a valid step in the solution process (this relates to choice C).
4. Divide to Solve for the Variable:
Finally, divide both sides of the equation by 12 to find [tex]\(x\)[/tex]:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
Simplifying gives:
[tex]\[
x = 4
\][/tex]
Dividing both sides by 12 to isolate [tex]\(x\)[/tex] is a crucial step in the process (this relates to choice A).
Given this breakdown, the step that is NOT part of the solution process is:
B. Simplifying by combining variable terms
This is because there was no need to combine variable terms in the given steps.
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