Chapter 4 - Polynomial and Rational Functions - 4.4 Polynomial and Rational Inequalities - 4.4 Assess Your Understanding - Page 219: 17

$(-2,-1]$

Step 1. Graph $R(x)=\frac{3x+3}{2x+4}$ as shown in the figure. Step 2. The vertical asymptote ($x=-2$) and a zero ($x=-1$) divide the x-axis into three intervals $(-\infty,-2),(-2,-1],[-1,\infty)$ Step 3. For $R(x)\le0$, we can identify the solution intervals as $(-2,-1]$