Honors Algebra 2: Extra Practice on Compound Inequalities

Solve the following:

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