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Section 2.13 : Rational Inequalities

Solve each of the following inequalities.

1. \( \displaystyle \frac{{t + 6}}{{t - 1}} < 0\)
2. \( \displaystyle \frac{{4x + 2}}{{3 - x}} \ge 0\)
3. \( \displaystyle \frac{{2u + 3}}{{u + 6}} > 0\)
4. \( \displaystyle \frac{{3 - z}}{{z + 1}} < - 2\)
5. \( \displaystyle \frac{{w + 9}}{{w + 2}} \le 3\)
6. \( \displaystyle \frac{{{x^2} + 9x + 14}}{{x - 1}} > 0\)
7. \( \displaystyle \frac{{4{z^2} + 3z - 10}}{z} \ge 0\)
8. \( \displaystyle \frac{{{t^2} + 10t + 16}}{{{t^2} - 4t + 3}} \le 0\)
9. \( \displaystyle \frac{{{z^2} - 6z + 4}}{{z - 5}} < 4\)
10. \( \displaystyle w - 5 \ge \frac{{3 - {w^2}}}{w}\)
11. \( \displaystyle \frac{{{x^2} + 8x + 16}}{x} > 0\)
12. \( \displaystyle \frac{{u - 8}}{{3{u^4} - {u^5}}} \le 0\)
13. \( \displaystyle \frac{2}{{{x^2} - 2x + 1}} \ge 0\)