Question

solve for $x$ and graph the solution on the number line below.
$-2x - 5geq3$ or $-7 > -2x - 5$

Explanation:

Step1: Solve the first inequality

Add 5 to both sides of $-2x - 5\geq3$:
$-2x-5 + 5\geq3 + 5$
$-2x\geq8$
Divide both sides by - 2 and reverse the inequality sign:
$x\leq - 4$

Step2: Solve the second inequality

Add 5 to both sides of $-7>-2x - 5$:
$-7+5>-2x-5 + 5$
$-2>-2x$
Divide both sides by - 2 and reverse the inequality sign:
$1 1$

Answer:

The solution is $x\leq - 4$ or $x>1$. On a number - line, we have a closed circle at $x = - 4$ and shade to the left for $x\leq - 4$, and an open circle at $x = 1$ and shade to the right for $x>1$.