We've updated our

TEXT

# Solutions

## 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. $|x - 5.0|\le 0.01$