Question

which graph shows the solution set for $-\frac{5}{2}x - 3 < 2$?

Explanation:

Step1: Solve the inequality

$$\begin{align*} -\frac{5}{2}x - 3 &< 2\\ -\frac{5}{2}x&<2 + 3\\ -\frac{5}{2}x&<5\\ x&>5\times(-\frac{2}{5})\\ x&>- 2 \end{align*}$$

Step2: Analyze the graph

When \(x>-2\), it is an open - circle at \(x = - 2\) (because the inequality is strict, \(x
eq-2\)) and the arrow points to the right (towards larger values of \(x\)).

Answer:

The graph with an open - circle at \(-2\) and an arrow pointing to the right.