Question

solve the compound inequality.
4x + 4 < -20 or 3x - 3 > 15
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 4 from both sides of $4x + 4 < - 20$:
$4x+4 - 4 < - 20 - 4$, which simplifies to $4x < - 24$. Then divide both sides by 4: $x < - 6$.

Step2: Solve the second inequality

Add 3 to both sides of $3x - 3>15$:
$3x-3 + 3>15 + 3$, which simplifies to $3x>18$. Then divide both sides by 3: $x > 6$.

Answer:

The solution of the compound - inequality is $x < - 6$ or $x>6$. On the number - line, we use an open circle at $x=-6$ and shade to the left, and use an open circle at $x = 6$ and shade to the right.