Alright, let's carefully go through each step of the given simplification process to identify the incorrect step.
1. The original equation is:
[tex]\[
2(x + 1) = 3(2x - 2)
\][/tex]
2. Step-1: Open the brackets.
[tex]\[
2(x + 1) = 3(2x - 2)
\][/tex]
Simplifying both sides:
[tex]\[
2x + 2 = 6x - 6
\][/tex]
This step is correct.
3. Step-2: Combine like terms by moving all [tex]\( x \)[/tex] terms to one side and constants to the other side.
[tex]\[
2x + 2 = 6x - 6
\][/tex]
Subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[
2 = 4x - 6
\][/tex]
Add [tex]\( 6 \)[/tex] to both sides:
[tex]\[
8 = 4x
\][/tex]
This step could be written clearly as [tex]\[ 2x + 2 + 6 = 6x - 6 + 6 \rightarrow 6x - 2x = 2 + 6 \rightarrow 4x = 8\][/tex], which is correct.
4. Step-3: Solve for [tex]\( x \)[/tex].
[tex]\[
4x = 8
\][/tex]
Divide both sides by 4:
[tex]\[
x = \frac{8}{4} = 2
\][/tex]
This step is correct.
5. Step-4: This step states:
[tex]\[
x = 32
\][/tex]
This is incorrect, because from step 3, we already found that [tex]\( x = 2 \)[/tex], not 32.
So, the incorrect step is:
(b) Step - 4
