Section 1.7 Homework

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Section 1.7 Homework

1. Solve the linear inequality. Express the solution using interval notation.

$3 x \leq 4$

Graph the solution set.

2. Solve the linear inequality. Express the solution using interval notation.

$- 7 < 1 - 2 x$

Graph the solution set.

3. Solve the linear inequality. Express the solution using interval notation.

$4 + 4 x \leq 8 - 2 x$

Graph the solution set.

4 Solve the linear inequality. Express the solution using interval notation.

$\frac{1}{2} x - \frac{1}{3} > 4$

Graph the solution set.

5. Solve the linear inequality. Express the solution using interval notation.

$2 (4 x - 3) \leq 6 x + 24$

6. Solve the linear inequality. Express the solution using interval notation.

$- 8 < 3 x - 9 < 9$

7. Solve the linear inequality. Express the solution using interval notation.

$- 4 \leq 3 x + 6 \leq \frac{1}{2}$

8. Solve the nonlinear inequality. Express the solution using interval notation.

$(x - 7) (x + 3) \geq 0$

9. Solve the nonlinear inequality. Express the solution using interval notation.

$x (2 x + 7) \geq 0$

10. Solve the nonlinear inequality. Express the solution using interval notation.

x^{2} + 9 x + 20 > 0

11. Solve the nonlinear inequality. Express the solution using interval notation.

2 x^{2} + x \geq 15

12. Solve the nonlinear inequality. Express the solution using interval notation.

5 x^{2} + 13 x \geq 3 x^{2} + 24

13. Solve the nonlinear inequality. Express the solution using interval notation.

$(x - 9) (x - 5) (x + 4) > 0$

14. Solve the nonlinear inequality. Express the solution using interval notation.

$\frac{x + 4}{2 x - 1} \geq 0$

15. Solve the nonlinear inequality. Express the solution using interval notation.

$- 3 < \frac{x + 1}{x - 5}$

16. Solve the nonlinear inequality. Express the solution using interval notation.

$\frac{x}{x + 1} > 5 x$

17. Solve the nonlinear inequality. Express the solution using interval notation.

$1 + \frac{2}{x + 1} \leq \frac{2}{x}$

18. Solve the nonlinear inequality. Express the solution using interval notation.

$\frac{x}{2} \geq \frac{9}{x + 1} + 1$

19. A telephone company offers two long-distance plans.

Plan A: $25 per month and 5¢ per minute
Plan B: $4 per month and 14¢ per minute

For how many minutes of long-distance calls would plan B be financially advantageous? (Assume the plan will be used for one month. Round your answer up to the nearest whole minute.)

Plan B is advantageous if a person places fewer than ____ minutes of long-distance calls during a month.

20 In the vicinity of a bonfire, the temperature T in °C at a distance of x meters from the center of the fire was given by

$T = \frac{3600000}{x^{2} + 275}$

At what range of distances from the fire’s center was the temperature less than 400°C?

The temperature will be less than 400°C at distances greater than ___ m from the center of the fire.

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This question is taken from Math 110A – PreCalculus I » Fall 2021 » Homeworks

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