Question

solve the compound inequality.
4x + 4 < - 8 or 4x - 2 ≥ 6
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 4 from both sides of $4x + 4<-8$.
$4x+4 - 4<-8 - 4$, which simplifies to $4x<-12$. Then divide both sides by 4: $x<-3$.

Step2: Solve the second inequality

Add 2 to both sides of $4x - 2\geq6$.
$4x-2 + 2\geq6 + 2$, which simplifies to $4x\geq8$. Then divide both sides by 4: $x\geq2$.

Step3: Graph - represent on number line

For $x < - 3$, we use an open - circle at $x=-3$ and an arrow pointing to the left. For $x\geq2$, we use a closed - circle at $x = 2$ and an arrow pointing to the right.

Answer:

The solution of the compound inequality is $x<-3$ or $x\geq2$. On the number line, there is an open circle at $-3$ with an arrow pointing left and a closed circle at $2$ with an arrow pointing right.