Question

solve the compound inequality.
2x - 2 ≤ - 8 or 4x + 1 > 25
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Add 2 to both sides of $2x - 2\leq - 8$:
$2x-2 + 2\leq - 8+2$, which simplifies to $2x\leq - 6$. Then divide both sides by 2: $x\leq - 3$.

Step2: Solve the second inequality

Subtract 1 from both sides of $4x + 1>25$:
$4x+1 - 1>25 - 1$, which simplifies to $4x>24$. Then divide both sides by 4: $x > 6$.

Answer:

The solution is $x\leq - 3$ or $x>6$. On the number - line, you would have a closed circle at $x = - 3$ and shade to the left, and an open circle at $x = 6$ and shade to the right.