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# Solutions

## 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 $x=-3$. [latex-display]\left(-\infty ,-3\right)[/latex-display] 41. Where the blue line is above the orange line; always. All real numbers. [latex-display]\left(-\infty ,-\infty \right)[/latex-display] 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. $\begin{array}{l}80\le T\le 120\\ 1,600\le 20T\le 2,400\end{array}$ [latex-display]\left[1,600, 2,400\right][/latex-display]