Question

solve the compound inequality.
2x - 3 ≥ 3 or 2x - 3 < -7
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Add 3 to both sides of $2x - 3\geq3$:
$2x-3 + 3\geq3 + 3$, which simplifies to $2x\geq6$. Then divide both sides by 2: $x\geq3$.

Step2: Solve the second inequality

Add 3 to both sides of $2x - 3<-7$:
$2x-3 + 3<-7 + 3$, which simplifies to $2x<-4$. Then divide both sides by 2: $x<-2$.

Answer:

The solution of the compound - inequality is $x < - 2$ or $x\geq3$. On the number - line, we have an open circle at $x=-2$ and shade to the left, and a closed circle at $x = 3$ and shade to the right.