Question

solve the compound inequality.
4x + 1 < - 3 or 3x - 3 ≥ 12
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 1 from both sides of $4x + 1 < - 3$:
$4x+1 - 1<-3 - 1$
$4x<-4$
Divide both sides by 4:
$x < - 1$

Step2: Solve the second inequality

Add 3 to both sides of $3x-3\geq12$:
$3x-3 + 3\geq12 + 3$
$3x\geq15$
Divide both sides by 3:
$x\geq5$

Answer:

The solution of the compound - inequality is $x < - 1$ or $x\geq5$. On the number - line, we have an open circle at $x=-1$ and an arrow pointing to the left for $x < - 1$, and a closed circle at $x = 5$ and an arrow pointing to the right for $x\geq5$.