Question

solve the compound inequality.
4x + 6 ≤ - 10 or 4x + 5>5
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Subtract 6 from both sides of $4x + 6\leq - 10$.
$4x+6 - 6\leq - 10 - 6$, which simplifies to $4x\leq - 16$. Then divide both sides by 4: $x\leq - 4$.

Step2: Solve the second inequality

Subtract 5 from both sides of $4x + 5>5$.
$4x+5 - 5>5 - 5$, which simplifies to $4x>0$. Then divide both sides by 4: $x>0$.

Answer:

The solution is $x\leq - 4$ or $x>0$. On the number - line, we have a closed circle at $x = - 4$ and shade to the left for $x\leq - 4$, and an open circle at $x = 0$ and shade to the right for $x>0$.