Solutions to Try Its

1. $|x - 2|\le 3$

2. using the variable $p$ for passing, $|p - 80|\le 20$

3. $f\left(x\right)=-|x+2|+3$

4. $x=-1$ or $x=2$

5. $f\left(0\right)=1$, so the graph intersects the vertical axis at $\left(0,1\right)$. $f\left(x\right)=0$ when $x=-5$ and $x=1$ so the graph intersects the horizontal axis at $\left(-5,0\right)$ and $\left(1,0\right)$.

6. $4\le x\le 8$

7. $k\le 1$ 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. Isolate the absolute value term so that the equation is of the form $|A|=B$. Form one equation by setting the expression inside the absolute value symbol, $A$, equal to the expression on the other side of the equation, $B$. Form a second equation by setting $A$ equal to the opposite of the expression on the other side of the equation, -B. Solve each equation for the variable.

3. The graph of the absolute value function does not cross the $x$ -axis, so the graph is either completely above or completely below the $x$ -axis.

5. First determine the boundary points by finding the solution(s) of the equation. Use the boundary points to form possible solution intervals. Choose a test value in each interval to determine which values satisfy the inequality.

7. $|x+4|=\frac{1}{2}$

9. $|f\left(x\right)-8|<0.03$

11. $\left\{1,11\right\}$

13. $\left\{\frac{9}{4},\frac{13}{4}\right\}$

15. $\left\{\frac{10}{3},\frac{20}{3}\right\}$

17. $\left\{\frac{11}{5},\frac{29}{5}\right\}$

19. $\left\{\frac{5}{2},\frac{7}{2}\right\}$

21. No solution

23. $\left\{-57,27\right\}$

25. $\left(0,-8\right);\left(-6,0\right),\left(4,0\right)$

27. $\left(0,-7\right)$; no $x$ -intercepts

29. $\left(-\infty ,-8\right)\cup \left(12,\infty \right)$

31. $\frac{-4}{3}\le x\le 4$

33. $\left(-\infty ,-\frac{8}{3}\right]\cup \left[6,\infty \right)$

35. $\left(-\infty ,-\frac{8}{3}\right]\cup \left[16,\infty \right)$

37.

39.

41.

43.

45.

47.

49.

51.

53. range: $\left[0,20\right]$

55. $x\text{-}$ intercepts:

57. $\left(-\infty ,\infty \right)$

59. There is no solution for $a$ that will keep the function from having a $y$ -intercept. The absolute value function always crosses the $y$ -intercept when $x=0$.

61. $|p - 0.08|\le 0.015$

63. $|x - 5.0|\le 0.01$