Question

which of the following number lines represents the solution set of the inequality? -5x - 4 < 3x + 12 ≤ 21

Explanation:

Step1: Split the compound - inequality

Split $-5x - 4<3x + 12\leq21$ into two inequalities: $-5x - 4<3x + 12$ and $3x + 12\leq21$.

Step2: Solve $-5x - 4<3x + 12$

Add $5x$ to both sides: $-4<8x + 12$. Then subtract 12 from both sides: $-16<8x$. Divide both sides by 8: $x>- 2$.

Step3: Solve $3x + 12\leq21$

Subtract 12 from both sides: $3x\leq9$. Divide both sides by 3: $x\leq3$.

Answer:

The solution set is $-2 < x\leq3$. The number - line with an open circle at $-2$ and a closed circle at 3 and the line segment in between represents the solution set. So, the correct number - line has an open circle at $-2$ and a closed circle at 3.