Question

solve the compound inequality.
4x + 2 < - 14 or 2x + 3 ≥ 1
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Solve $4x + 2 < - 14$. Subtract 2 from both sides: $4x+2 - 2< - 14 - 2$, which gives $4x<-16$. Then divide both sides by 4: $x < - 4$.

Step2: Solve the second inequality

Solve $2x + 3\geq1$. Subtract 3 from both sides: $2x+3 - 3\geq1 - 3$, which gives $2x\geq - 2$. Then divide both sides by 2: $x\geq - 1$.

Answer:

The solution is $x < - 4$ or $x\geq - 1$. On the number - line, we have an open circle at $x = - 4$ and an arrow pointing to the left for $x < - 4$, and a closed circle at $x=-1$ and an arrow pointing to the right for $x\geq - 1$.