Question

solve the inequality for x.
$5 - \frac{3}{2}x \geq \frac{1}{3}$
a. $x \leq \frac{28}{9}$
b. $x \leq 7$
c. $x \geq \frac{28}{9}$
d. $x \geq 7$

Explanation:

Step1: Subtract 5 from both sides

$5 - \frac{3}{2}x - 5 \geq \frac{1}{3} - 5$
$-\frac{3}{2}x \geq \frac{1}{3} - \frac{15}{3}$
$-\frac{3}{2}x \geq -\frac{14}{3}$

Step2: Multiply by reciprocal, reverse inequality

$x \leq -\frac{14}{3} \times (-\frac{2}{3})$
$x \leq \frac{28}{9}$

Answer:

A. $x \leq \frac{28}{9}$