Question

solve the compound inequality.
4x + 6 < -6 or 4x + 1 ≥ 21
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 6 from both sides of $4x + 6 < - 6$.
$4x+6 - 6 < - 6 - 6$
$4x < - 12$
Then divide both sides by 4: $x < - 3$.

Step2: Solve the second inequality

Subtract 1 from both sides of $4x + 1\geq21$.
$4x+1 - 1\geq21 - 1$
$4x\geq20$
Then divide both sides by 4: $x\geq5$.

Answer:

The solution of the compound - inequality is $x < - 3$ or $x\geq5$. On the number - line, we have an open circle at $x=-3$ and shade to the left for $x < - 3$, and a closed circle at $x = 5$ and shade to the right for $x\geq5$.