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1. Select the incorrect step in the simplification of [tex]$2(x+1)=3(2x-2)$[/tex]:

Step 1: [tex]2x + 2 = 6x - 6[/tex] (open brackets)

Step 2: [tex]6x - 2x = 2 + 6[/tex] (combining like terms)

Step 3: [tex]4x = 8[/tex]

Step 4: [tex]x = 32[/tex] (multiplying by 4 on both sides)

(a) Step 2

(b) Step 4

(c) Step 3

(d) Step 1


Sagot :

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