Let us analyze and correct the given steps in solving the equation:
The original equation is:
[tex]\[ -2(7 - y) + 4 = -4 \][/tex]
Let's solve this equation step-by-step:
### Step 1: Distribute the -2
Multiply both terms inside the parentheses by -2:
[tex]\[ -2 \cdot 7 + (-2) \cdot (-y) + 4 = -4 \][/tex]
[tex]\[ -14 + 2y + 4 = -4 \][/tex]
### Step 2: Combine like terms
Combine the constant terms on the left side:
[tex]\[ -14 + 4 + 2y = -4 \][/tex]
[tex]\[ -10 + 2y = -4 \][/tex]
### Step 3: Isolate the term involving [tex]\( y \)[/tex]
Add 10 to both sides to isolate the [tex]\( y \)[/tex]-term:
[tex]\[ -10 + 2y + 10 = -4 + 10 \][/tex]
[tex]\[ 2y = 6 \][/tex]
### Step 4: Solve for [tex]\( y \)[/tex]
Divide both sides by 2:
[tex]\[ y = \frac{6}{2} \][/tex]
[tex]\[ y = 3 \][/tex]
### Conclusion:
The error in the provided process occurred during the transition from the equation [tex]\(-10 - 2y = -4\)[/tex] to [tex]\(-2y = 6\)[/tex]. The correct algebraic steps show that [tex]\( y \)[/tex] should equal 3, not -3.
Therefore, the correct value of [tex]\( y \)[/tex] is:
[tex]\[ y = 3 \][/tex]
