Solve the given inequality. Write the solution set using interval notation, then graph it. \( \frac{3-2 x}{5} \geq-2 \)

Solve the equation \( \frac{3-2x}{5} \geq -2 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(\frac{3-2x}{5}\geq -2\) - step1: Multiply both sides: \(\frac{3-2x}{5}\times 5\geq -2\times 5\) - step2: Multiply the terms: \(3-2x\geq -10\) - step3: Move the constant to the right side: \(-2x\geq -10-3\) - step4: Subtract the numbers: \(-2x\geq -13\) - step5: Change the signs: \(2x\leq 13\) - step6: Divide both sides: \(\frac{2x}{2}\leq \frac{13}{2}\) - step7: Divide the numbers: \(x\leq \frac{13}{2}\) The solution to the inequality \( \frac{3-2x}{5} \geq -2 \) is \( x \leq \frac{13}{2} \). To graph this solution set, we need to plot the line \( x = \frac{13}{2} \) on the number line and shade the region to the left of the line, as the inequality is less than or equal to. The solution set in interval notation is \( (-\infty, \frac{13}{2}] \).