Question

solve for $x$ and graph the solution on the number line below.
$19 < -4x - 9$ or $-4x - 9 < -13$

Explanation:

Step1: Solve the first inequality

Add 9 to both sides of $19 < - 4x-9$:
$19 + 9< - 4x-9 + 9$, which simplifies to $28 < - 4x$. Then divide both sides by - 4. When dividing an inequality by a negative number, the inequality sign flips. So we have $x<-7$.

Step2: Solve the second inequality

Add 9 to both sides of $-4x - 9 < - 13$:
$-4x-9 + 9 < - 13+9$, which simplifies to $-4x < - 4$. Divide both sides by - 4. Since we are dividing by a negative number, the inequality sign flips, giving $x > 1$.

Answer:

The solution is $x < - 7$ or $x>1$. On a number - line, we would have an open circle at $x = - 7$ and shade to the left, and an open circle at $x = 1$ and shade to the right.