Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 159: 42

$[-\frac{4}{3},1]$

Step 1. Rewrite the inequality as $3x^2+x-4\le0$ Step 2. Factor the quadratic, we have $(x-1)(3x+4)\le0$ Step 3. The boundary points are $x=-\frac{4}{3}$ and $x=1$ Step 4. Use test points at $x=-2, 0, 2$, the signs of the quadratic are $+, -, +$ Step 5. The inequality requires negative, thus the solutions are $[-\frac{4}{3},1]$