Answer
$x \geq -\frac{33}{2}$
Work Step by Step
Collect constants on the right side of the inequality by subtracting $7$ from each side of the inequality:
$\frac{4x}{3} \geq -22$
Multiply each side by $3$ to get rid of the fraction:
$4x \geq -66$
Divide each side by $4$ to solve for $x$:
$x \geq -\frac{66}{4}$
Simplify the fraction by dividing the numerator and denominator by their greatest common factor, $2$:
$x \geq -\frac{33}{2}$
Let's check our answer by substituting our value for $x$ into the original inequality to see if our inequality holds true:
$7 + \frac{4(-\frac{33}{2})}{3} \geq -15$
Multiply:
$7 - \frac{66}{3} \geq -15$
Simplify the fraction:
$7 - 22 \geq -15$
Subtract:
$-15 \geq -15$
The inequality is true; therefore, our solution is correct.
