Question

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

Explanation:

Step1: Isolate the term with x

Add 3 to both sides of the inequality $-\frac{5}{2}x - 3\leq2$.
$-\frac{5}{2}x-3 + 3\leq2 + 3$
$-\frac{5}{2}x\leq5$

Step2: Solve for x

Multiply both sides by $-\frac{2}{5}$. When multiplying or dividing an inequality by a negative number, the direction of the inequality sign changes.
$x\geq5\times(-\frac{2}{5})$
$x\geq - 2$

Answer:

The solution set is all real - numbers greater than or equal to - 2. So the graph with a closed circle at - 2 and an arrow pointing to the right (the fourth option in the list of graphs) shows the solution set.