Question

solve the compound inequality.
2x + 4 < -4 or 3x + 1 > 10
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 4 from both sides of $2x + 4 < - 4$.
$2x+4 - 4<-4 - 4$, which simplifies to $2x<-8$. Then divide both sides by 2: $x < - 4$.

Step2: Solve the second inequality

Subtract 1 from both sides of $3x + 1>10$.
$3x+1 - 1>10 - 1$, which simplifies to $3x>9$. Then divide both sides by 3: $x > 3$.

Answer:

The solution of the compound - inequality is $x < - 4$ or $x>3$. On the number line, we have an open circle at $x = - 4$ and shade to the left, and an open circle at $x = 3$ and shade to the right.