Question

solve the compound inequality and choose the correct answer below. -4x - 1 > 15 or 5x - 3 ≥ - 8

Explanation:

Step1: Solve the first - inequality

Solve $-4x - 1>15$. Add 1 to both sides: $-4x>15 + 1$, so $-4x>16$. Divide both sides by - 4 and reverse the inequality sign: $x<-4$.

Step2: Solve the second - inequality

Solve $5x-3\geq - 8$. Add 3 to both sides: $5x\geq - 8 + 3$, so $5x\geq - 5$. Divide both sides by 5: $x\geq - 1$.

Step3: Analyze the solution on the number - line

The solution of $x<-4$ is all numbers to the left of - 4 (open circle at - 4) and the solution of $x\geq - 1$ is all numbers to the right of - 1 (closed circle at - 1).

Answer:

The first option (where the blue arrow points left from an open - circle at - 4 and the red arrow points right from a closed - circle at - 1) is correct.