Chapter 3 - Section 3.7 - Polynomial and Rational Inequalities - 3.7 Exercises - Page 316: 18

$(-2, 7/3]$

$\frac{3x+7}{x+2} \leq 0$ Find the zeros of the expressions in the numerator AND the denominator $x = 7/3, -2$ Test numbers in between those zero values to determine if the function is negative or positive (-∞, -2) $\frac{(-)}{(-)} = (+)$ (-2, 7/3] $\frac{(-)}{(+)} = (-)$ [-7/3, ∞) $\frac{(+)}{(+)} = (+)$ Thus the solution is $(-2, 7/3]$