Answer
The greatest integer solution is $0$.
Work Step by Step
First, we add $3$ to each side of the inequality:
$|-2x - 5| \leq 5$
To get rid of the absolute value sign, we use the definition of absolute value to rewrite the inequality as two inequalities such that the value of $-2x - 5$ is between $-5$ and $5$:
$-2x - 5 \geq -5$ and $-2x - 5 \leq 5$
Add $5$ to each side of the inequality:
$-2x \geq 0$ and $-2x \leq 10$
Divide each side of the inequality by $-2$. Remember that when we divide by a negative number, we need to reverse the signs:
$x \leq 0$ and $x \geq -5$
The greatest integer solution is $0$ because $x$ cannot be greater than $0$.
