## Solutions to Try Its

1. $\left[-3,5\right]$

2. $\left(-\infty ,-2\right)\cup \left[3,\infty \right)$

3. $x<1$

4. $x\ge -5$

5. $\left(2,\infty \right)$

6. $\left[-\frac{3}{14},\infty \right)$

7. $6<x\le 9\text{ }\text{ }\text{or}\left(6,9\right]$

8. $\left(-\frac{1}{8},\frac{1}{2}\right)$

9. $|x - 2|\le 3$

10. $k\le 1$ or $k\ge 7$; in interval notation, this would be $\left(-\infty ,1\right]\cup \left[7,\infty \right)$.

## Solutions to Odd-Numbered Exercises

1. When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.

3. $\left(-\infty ,\infty \right)$

5. We start by finding the x-intercept, or where the function = 0. Once we have that point, which is $\left(3,0\right)$, we graph to the right the straight line graph $y=x - 3$, and then when we draw it to the left we plot positive y values, taking the absolute value of them.

7. $\left(-\infty ,\frac{3}{4}\right]$

9. $\left[\frac{-13}{2},\infty \right)$

11. $\left(-\infty ,3\right)$

13. $\left(-\infty ,-\frac{37}{3}\right]$

15. All real numbers $\left(-\infty ,\infty \right)$

17. $\left(-\infty ,\frac{-10}{3}\right)\cup \left(4,\infty \right)$

19. $\left(-\infty ,-4\right]\cup \left[8,+\infty \right)$

21. No solution

23. $\left(-5,11\right)$

25. $\left[6,12\right]$

27. $\left[-10,12\right]$

29. $\begin{array}{ll}x> -6\text{ and }x> -2\hfill & \text{Take the intersection of two sets}.\hfill \\ x>-2,\text{ }\left(-2,+\infty \right)\hfill & \hfill \end{array}$

31. $\begin{array}{ll}x< -3\text{ }\mathrm{or}\text{ }x\ge 1\hfill & \text{Take the union of the two sets}.\hfill \\ \left(-\infty ,-3\right){\cup }\left[1,\infty \right)\hfill & \hfill \end{array}$

33. $\left(-\infty ,-1\right)\cup \left(3,\infty \right)$

35. $\left[-11,-3\right]$

37. It is never less than zero. No solution.

39. Where the blue line is above the orange line; point of intersection is $x=-3$.
$\left(-\infty ,-3\right)$

41. Where the blue line is above the orange line; always. All real numbers.
$\left(-\infty ,-\infty \right)$

43. $\left(-1,3\right)$

45. $\left(-\infty ,4\right)$

47. $\{x|x<6\}$

49. $\{x|-3\le x<5\}$

51. $\left(-2,1\right]$

53. $\left(-\infty ,4\right]$

55. Where the blue is below the orange; always. All real numbers. $\left(-\infty ,+\infty \right)$.

57. Where the blue is below the orange; $\left(1,7\right)$.

59. $x=2,\frac{-4}{5}$

61. $\left(-7,5\right]$

63. $\begin{array}{l}80\le T\le 120\\ 1,600\le 20T\le 2,400\end{array}$
$\left[1,600, 2,400\right]$