Question

solve the compound inequality.
4x + 3 < - 17 or 3x - 4 ≥ 11
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 3 from both sides of $4x + 3 < - 17$:
$4x+3 - 3< - 17 - 3$, which simplifies to $4x<-20$. Then divide both sides by 4: $x < - 5$.

Step2: Solve the second inequality

Add 4 to both sides of $3x - 4\geq11$:
$3x-4 + 4\geq11 + 4$, which simplifies to $3x\geq15$. Then divide both sides by 3: $x\geq5$.

Answer:

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