Honors Algebra 2: Extra Practice on Compound Inequalities

• Class: Honors Algebra 2
• Author: Peter Atlas
• Text: Algebra and Trigonometry: Structure and Method, Brown

Solve the following:

1. $$3x + 5 < 7x - 1 \leq 12x - 10$$
2. Solution $$\displaystyle x \geq \frac{9}{5}$$
3. $$2x+3 > 6x - 4\text{ or }5x + 9 < 15x - 8$$
4. Solution all real numbers
5. $$\displaystyle 2x + 1 \leq \frac{3 - 6x}{4} < \frac{5x}{3} + 2$$
6. Solution $$\displaystyle -\frac{15}{38} < x \leq -\frac{1}{14}$$
7. $$0.2x - 1 < 6\text{ or }1.5 - 3x \geq 4$$
8. Solution $$x < 35$$
9. $$4x + 10 > 12\text{ and }3x - 5 \geq 16$$
10. Solution $$x \geq 7$$
11. $$7x + 1 < 15\text{ and }12x + 10 > 42$$
12. Solution $$\emptyset$$
13. $$8 \left| 10x - 6 \right| - 16 < 24$$
14. Solution $$\displaystyle \frac{1}{10} < x < \frac{11}{10}$$
15. $$-5\left| x + 20 \right| - 15 > -35$$
16. Solution $$-24 < x < -16$$
17. $$\displaystyle \left| \frac{2x + 3}{8}\right| \geq 2$$
18. Solution $$\displaystyle x \leq -\frac{19}{2}\text{ or }x \geq \frac{23}{2}$$
19. $$\left|x + 5\right| + \left|x - 7\right| > 10$$
20. Solution all real numbers
21. $$\left|2x + 4\right| - \left|6x + 24\right| > 48$$
22. Solution $$\emptyset$$