Question

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

Explanation:

Step1: Solve the inequality

Solve \(-\frac{5}{2}x - 3\leq2\). First, add 3 to both sides: \(-\frac{5}{2}x\leq2 + 3\), so \(-\frac{5}{2}x\leq5\).

Step2: Isolate the variable

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

Step3: Interpret the solution on a number - line

The solution \(x\geq - 2\) is represented on a number - line with a closed circle at \(x=-2\) (because the inequality is \(\geq\), meaning \(-2\) is included in the solution set) and an arrow pointing to the right.

Answer:

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