Question

solve the compound inequality.
3x + 4 > 22 or 3x + 6 ≤ 12
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 4 from both sides of $3x + 4>22$:
$3x+4 - 4>22 - 4$
$3x>18$
Then divide both sides by 3:
$x > 6$

Step2: Solve the second inequality

Subtract 6 from both sides of $3x + 6\leq12$:
$3x+6 - 6\leq12 - 6$
$3x\leq6$
Then divide both sides by 3:
$x\leq2$

Step3: Graph on number - line

The solution of $x > 6$ is an open - circle at 6 and a ray to the right. The solution of $x\leq2$ is a closed - circle at 2 and a ray to the left.

Answer:

The solution of the compound inequality is $x\leq2$ or $x > 6$. On the number - line, there is a closed circle at 2 with a ray extending to the left and an open circle at 6 with a ray extending to the right.