Question

solve the linear equation for y.
if no solution exists, enter no solution. if the equation has infinite solutions, enter all real numbers.
$-(y + 12) = -4(y - 12) - 84$
show your work here

Explanation:

Step1: Distribute the negatives

First, we distribute the negative sign on the left side and the -4 on the right side.
For the left side: $-(y + 12) = -y - 12$
For the right side: $-4(y - 12) - 84 = -4y + 48 - 84 = -4y - 36$
So now our equation is: $-y - 12 = -4y - 36$

Step2: Add 4y to both sides

Adding 4y to both sides to get rid of the -4y on the right.
$-y - 12 + 4y = -4y - 36 + 4y$
Simplifying both sides: $3y - 12 = -36$

Step3: Add 12 to both sides

Adding 12 to both sides to isolate the term with y.
$3y - 12 + 12 = -36 + 12$
Simplifying: $3y = -24$

Step4: Divide by 3

Divide both sides by 3 to solve for y.
$\frac{3y}{3} = \frac{-24}{3}$
Simplifying: $y = -8$

Answer:

$y = -8$