Section 4.4: Unit 3 Practice Answers
- Page ID
- 192830
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Section 3.1P: Absolute Value
- \( y = \left\{ \begin{array}{ll} -x-1, & \text{if } x < -1 \\ x+1, & \text{if } x \ge -1 \end{array} \right. \)

- \( y = \left\{ \begin{array}{ll} 4-5x, & \text{if } x < \tfrac{4}{5} \\ -4+5x, & \text{if } x \ge \tfrac{4}{5} \end{array} \right. \)

- \( y = \left\{ \begin{array}{ll} -x-5, & \text{if } x < -5 \\ x+5, & \text{if } x \ge -5 \end{array} \right. \)

- \( y = \left\{ \begin{array}{ll} 0, & \text{if } x < 0 \\ 2x, & \text{if } x \ge 0 \end{array} \right. \)

- \( y = \left\{ \begin{array}{ll} -x+1, & \text{if } x < 1 \\ x-1, & \text{if } x \ge 1 \end{array} \right. \)

- \( y = \left\{ \begin{array}{ll} -2x+1, & \text{if } x < \tfrac{1}{2} \\ 2x-1, & \text{if } x \ge \tfrac{1}{2} \end{array} \right. \)

- \( y = \left\{ \begin{array}{ll} 1-3x, & \text{if } x < \tfrac{1}{3} \\ -1+3x, & \text{if } x \ge \tfrac{1}{3} \end{array} \right. \)

- \( y = \left\{ \begin{array}{ll} 2x, & \text{if } x < 0 \\ 0, & \text{if } x \ge 0 \end{array} \right. \)

- Answers will vary.
- Answers will vary.
Section 3.2P: Absolute Value Equations
- \(x=3,x=−3\)
- no solution
- \(z=0\)
- \(x=1, x=4\)
- \(x=1, \,x=−\frac{1}{2}\)
- \(x=\tfrac{2}{3}, x=2\)
- \(x=−1, \,x=−\frac{5}{2}\)
- \(x=-1, x=3\)
- \(x=7, \,x=1\)
- \(x=0, x=\tfrac{5}{2}\)
- \(x=1, \,x=−5\)
- \(x=-3, x=9\)
- \(x=7, \,x=1\)
- no solution
- no solution
- \(x=−1, \,x=−\frac{2}{3}\)
- \(x=−3, \,x=3\)
- Answers will vary.
Section 3.3P: Absolute Value Inequalities
- \((-5,5)\)
- \((-1,1)\)
- \([-3,3]\)
- \([-1,3]\)
- \([1,4]\)
- \((-\infty,-6)\cup(6,\infty)\)
- \((-\infty,-2]\cup[2,\infty)\)
- \((-\infty,-5\cup[5,\infty)\)
- \((-\infty,\infty)\)
- \((-\infty,-\tfrac{2}{3})\cup(2,\infty)\)
- No Solution
- No Solution
- \(\left(-\tfrac{1}{3},2\right)\)
- No Solution
- \((-\infty,-2)\cup(3,\infty)\)
- \((-\infty,6]\cup[8,\infty)\)
- \((-\infty,\infty)\)
- \((-\infty,\infty)\)
- The minimum to maximum expected production is 207,500 to 2,225,000 bottles.
- The acceptable weight is 22.5 to 25.5 ounces.
- Answers will vary.


