Answer :
Let's analyze the steps provided to solve the equation [tex]\(4(3x - 6) = 24\)[/tex]:
Step 1:
[tex]\[
4(3x - 6) = 24
\][/tex]
- Here, the equation is in its original form.
Step 2:
[tex]\[
12x - 24 = 24
\][/tex]
- This step involves using the distributive property to expand [tex]\(4(3x - 6)\)[/tex] into [tex]\(12x - 24\)[/tex].
Step 3:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
- This step involves adding 24 to both sides of the equation to eliminate the constant term on the left side.
Step 4:
[tex]\[
12x = 48
\][/tex]
- Simplifying the equation after adding 24 to both sides.
Step 5:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
- Here, we divide both sides by 12 to isolate the variable [tex]\(x\)[/tex].
Step 6:
[tex]\[
x = 4
\][/tex]
- Solving for [tex]\(x\)[/tex].
Let's determine which of the given options are part of the solution process:
A. Using the distributive property:
- This is clearly part of the solution process in Step 2.
B. Dividing both sides by 12 to isolate the variable:
- This happens in Step 5.
C. Adding 24 to both sides to isolate the variable term:
- This is done in Step 3.
D. Simplifying by combining variable terms:
- We do not see any step combining variable terms. All the steps involve simplifying or isolating terms.
Therefore, the step that is NOT part of the solution process is:
D. Simplifying by combining variable terms
Step 1:
[tex]\[
4(3x - 6) = 24
\][/tex]
- Here, the equation is in its original form.
Step 2:
[tex]\[
12x - 24 = 24
\][/tex]
- This step involves using the distributive property to expand [tex]\(4(3x - 6)\)[/tex] into [tex]\(12x - 24\)[/tex].
Step 3:
[tex]\[
12x - 24 + 24 = 24 + 24
\][/tex]
- This step involves adding 24 to both sides of the equation to eliminate the constant term on the left side.
Step 4:
[tex]\[
12x = 48
\][/tex]
- Simplifying the equation after adding 24 to both sides.
Step 5:
[tex]\[
\frac{12x}{12} = \frac{48}{12}
\][/tex]
- Here, we divide both sides by 12 to isolate the variable [tex]\(x\)[/tex].
Step 6:
[tex]\[
x = 4
\][/tex]
- Solving for [tex]\(x\)[/tex].
Let's determine which of the given options are part of the solution process:
A. Using the distributive property:
- This is clearly part of the solution process in Step 2.
B. Dividing both sides by 12 to isolate the variable:
- This happens in Step 5.
C. Adding 24 to both sides to isolate the variable term:
- This is done in Step 3.
D. Simplifying by combining variable terms:
- We do not see any step combining variable terms. All the steps involve simplifying or isolating terms.
Therefore, the step that is NOT part of the solution process is:
D. Simplifying by combining variable terms