Question

solve the compound inequality.
4x - 6 ≤ -22 or 4x + 4 > 20
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Add 6 to both sides of $4x - 6\leq - 22$.
$4x-6 + 6\leq-22 + 6$, which simplifies to $4x\leq-16$. Then divide both sides by 4: $x\leq-4$.

Step2: Solve the second inequality

Subtract 4 from both sides of $4x + 4>20$.
$4x+4 - 4>20 - 4$, which simplifies to $4x>16$. Then divide both sides by 4: $x > 4$.

Answer:

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