Answer
$-4$
Work Step by Step
Add $6$ to each side of the equation:
$|2x + 4| = 14$
To get rid of the absolute value signs, rewrite the equation as two equations, using the definition of absolute value, which is $|x|=a \implies x= a \quad \text{or} \quad x=-a$:
$2x + 4 = 14\quad$ or $\quad2x + 4 = -14$
Subtract $4$ from each side of the equation:
$2x = 10\quad$ or $\quad2x = -18$
Divide both sides by $2$ to solve for $x$:
$x = 5\quad$ or $\quad x = -9$
In this exercise, we are not asked for the solution; instead, we are asked to give the sum of the answers, so we simply add our solutions together:
$5 + (-9) = -4$
The solution to this exercise is $-4$.
