Stewart Precalc 6e Section 1.7: Inequalities

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Stewart Precalc 6e Section 1.7: Inequalities 0/126
1 Concept - Inequality Properties · Level 1
Fill in the blank with an appropriate inequality sign. (a) If \(x < 5\), then \(x - 3\) ___ \(2\). (b) If \(x \leq 5\), then \(3x\) ___ \(15\). (c) If \(x \geq 2\), then \(-3x\) ___ \(-6\). (d) If \(x < -2\), then \(-x\) ___ \(2\).
2 Concept - True/False · Level 1
True or false? (a) If \(x(x + 1) > 0\), then \(x\) and \(x + 1\) are either both positive or both negative. (b) If \(x(x + 1) > 5\), then \(x\) and \(x + 1\) are each greater than 5.
3 Concept - Absolute Value Solution · Level 1
(a) The solution of the inequality \(|x| \leq 3\) is the interval ___. (b) The solution of the inequality \(|x| \geq 3\) is a union of two intervals ___ \(\cup\) ___.
4 Concept - Absolute Value Description · Level 1
(a) The set of all points on the real line whose distance from zero is less than 3 can be described by the absolute value inequality \(|x|\) ___ \(3\). (b) The set of all points on the real line whose distance from zero is greater than 3 can be described by the absolute value inequality \(|x|\) ___ \(3\).
5 Skills - Testing Elements · Level 1
Let \(S = {-2, -1, 0, \dfrac{1}{2}, 1, \sqrt{2}, 2, 4}\). Determine which elements of \(S\) satisfy the inequality \(3 - 2x \leq \dfrac{1}{2}\).
6 Skills - Testing Elements · Level 1
Let \(S = {-2, -1, 0, \dfrac{1}{2}, 1, \sqrt{2}, 2, 4}\). Determine which elements of \(S\) satisfy the inequality \(2x - 1 \geq x\).
7 Skills - Testing Elements · Level 1
Let \(S = {-2, -1, 0, \dfrac{1}{2}, 1, \sqrt{2}, 2, 4}\). Determine which elements of \(S\) satisfy the inequality \(1 < 2x - 4 \leq 7\).
8 Skills - Testing Elements · Level 1
Let \(S = {-2, -1, 0, \dfrac{1}{2}, 1, \sqrt{2}, 2, 4}\). Determine which elements of \(S\) satisfy the inequality \(-2 \leq 3 - x < 2\).
9 Skills - Testing Elements · Level 2
Let \(S = {-2, -1, 0, \dfrac{1}{2}, 1, \sqrt{2}, 2, 4}\). Determine which elements of \(S\) satisfy the inequality \(\dfrac{1}{x} \leq \dfrac{1}{2}\).
10 Skills - Testing Elements · Level 1
Let \(S = {-2, -1, 0, \dfrac{1}{2}, 1, \sqrt{2}, 2, 4}\). Determine which elements of \(S\) satisfy the inequality \(x^2 + 2 < 4\).
11 Skills - Linear Inequality · Level 1
Solve the linear inequality \(2x \leq 7\). Express the solution using interval notation and graph the solution set.
12 Skills - Linear Inequality · Level 1
Solve the linear inequality \(-4x \geq 10\). Express the solution using interval notation and graph the solution set.
13 Skills - Linear Inequality · Level 1
Solve the linear inequality \(2x - 5 > 3\). Express the solution using interval notation and graph the solution set.
14 Skills - Linear Inequality · Level 1
Solve the linear inequality \(3x + 11 < 5\). Express the solution using interval notation and graph the solution set.
15 Skills - Linear Inequality · Level 1
Solve the linear inequality \(7 - x \geq 5\). Express the solution using interval notation and graph the solution set.
16 Skills - Linear Inequality · Level 1
Solve the linear inequality \(5 - 3x \leq -16\). Express the solution using interval notation and graph the solution set.
17 Skills - Linear Inequality · Level 1
Solve the linear inequality \(2x + 1 < 0\). Express the solution using interval notation and graph the solution set.
18 Skills - Linear Inequality · Level 1
Solve the linear inequality \(0 < 5 - 2x\). Express the solution using interval notation and graph the solution set.
19 Skills - Linear Inequality · Level 1
Solve the linear inequality \(3x + 11 \leq 6x + 8\). Express the solution using interval notation and graph the solution set.
20 Skills - Linear Inequality · Level 1
Solve the linear inequality \(6 - x \geq 2x + 9\). Express the solution using interval notation and graph the solution set.
21 Skills - Linear Inequality · Level 2
Solve the linear inequality \(\dfrac{1}{2}x - \dfrac{2}{3} > 2\). Express the solution using interval notation and graph the solution set.
22 Skills - Linear Inequality · Level 2
Solve the linear inequality \(\dfrac{2}{5}x + 1 < \dfrac{1}{5} - 2x\). Express the solution using interval notation and graph the solution set.
23 Skills - Linear Inequality · Level 2
Solve the linear inequality \(\dfrac{1}{3}x + 2 < \dfrac{1}{6}x - 1\). Express the solution using interval notation and graph the solution set.
24 Skills - Linear Inequality · Level 2
Solve the linear inequality \(\dfrac{2}{3} - \dfrac{1}{2}x \geq \dfrac{1}{6} + x\). Express the solution using interval notation and graph the solution set.
25 Skills - Linear Inequality · Level 1
Solve the linear inequality \(4 - 3x \leq -(1 + 8x)\). Express the solution using interval notation and graph the solution set.
26 Skills - Linear Inequality · Level 1
Solve the linear inequality \(2(7x - 3) \leq 12x + 16\). Express the solution using interval notation and graph the solution set.
27 Skills - Compound Inequality · Level 1
Solve the linear inequality \(2 \leq x + 5 < 4\). Express the solution using interval notation and graph the solution set.
28 Skills - Compound Inequality · Level 1
Solve the linear inequality \(5 \leq 3x - 4 \leq 14\). Express the solution using interval notation and graph the solution set.
29 Skills - Compound Inequality · Level 1
Solve the linear inequality \(-1 < 2x - 5 < 7\). Express the solution using interval notation and graph the solution set.
30 Skills - Linear Inequality · Level 1
Solve the linear inequality \(1 < 5x + 1\). Express the solution using interval notation and graph the solution set.
31 Skills - Compound Inequality · Level 2
Solve the linear inequality \(-2 < 8 - 2x \leq -1\). Express the solution using interval notation and graph the solution set.
32 Skills - Compound Inequality · Level 2
Solve the linear inequality \(-3 \leq 3x + 7 \leq \dfrac{1}{2}\). Express the solution using interval notation and graph the solution set.
33 Skills - Compound Inequality · Level 2
Solve the linear inequality \(\dfrac{1}{6} < \dfrac{2x - 13}{12} \leq \dfrac{2}{3}\). Express the solution using interval notation and graph the solution set.
34 Skills - Compound Inequality · Level 2
Solve the linear inequality \(-\dfrac{1}{2} \leq \dfrac{4 - 3x}{5} \leq \dfrac{1}{4}\). Express the solution using interval notation and graph the solution set.
35 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \((x + 2)(x - 3) < 0\). Express the solution using interval notation and graph the solution set.
36 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \((x - 5)(x + 4) \geq 0\). Express the solution using interval notation and graph the solution set.
37 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(x(2x + 7) \geq 0\). Express the solution using interval notation and graph the solution set.
38 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(x(2 - 3x) \leq 0\). Express the solution using interval notation and graph the solution set.
39 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(x^2 - 3x - 18 \leq 0\). Express the solution using interval notation and graph the solution set.
40 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(x^2 + 5x + 6 > 0\). Express the solution using interval notation and graph the solution set.
41 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(2x^2 + x \geq 1\). Express the solution using interval notation and graph the solution set.
42 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(x^2 < x + 2\). Express the solution using interval notation and graph the solution set.
43 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(3x^2 - 3x < 2x^2 + 4\). Express the solution using interval notation and graph the solution set.
44 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(5x^2 + 3x \geq 3x^2 + 2\). Express the solution using interval notation and graph the solution set.
45 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(x^2 > 3(x + 6)\). Express the solution using interval notation and graph the solution set.
46 Skills - Nonlinear Inequality · Level 2
Solve the nonlinear inequality \(x^2 + 2x > 3\). Express the solution using interval notation and graph the solution set.
47 Skills - Nonlinear Inequality · Level 1
Solve the nonlinear inequality \(x^2 < 4\). Express the solution using interval notation and graph the solution set.
48 Skills - Nonlinear Inequality · Level 1
Solve the nonlinear inequality \(x^2 \geq 9\). Express the solution using interval notation and graph the solution set.
49 Skills - Cubic Inequality · Level 3
Solve the nonlinear inequality \((x + 2)(x - 1)(x - 3) \leq 0\). Express the solution using interval notation and graph the solution set.
50 Skills - Cubic Inequality · Level 3
Solve the nonlinear inequality \((x - 5)(x - 2)(x + 1) > 0\). Express the solution using interval notation and graph the solution set.
51 Skills - Repeated Factor · Level 3
Solve the nonlinear inequality \((x - 4)(x + 2)^2 < 0\). Express the solution using interval notation and graph the solution set.
52 Skills - Repeated Factor · Level 3
Solve the nonlinear inequality \((x + 3)^2(x + 1) > 0\). Express the solution using interval notation and graph the solution set.
53 Skills - Repeated Factor · Level 3
Solve the nonlinear inequality \((x - 2)^2(x - 3)(x + 1) \leq 0\). Express the solution using interval notation and graph the solution set.
54 Skills - Repeated Factor · Level 3
Solve the nonlinear inequality \(x^2(x^2 - 1) \geq 0\). Express the solution using interval notation and graph the solution set.
55 Skills - Cubic Inequality · Level 3
Solve the nonlinear inequality \(x^3 - 4x > 0\). Express the solution using interval notation and graph the solution set.
56 Skills - Cubic Inequality · Level 3
Solve the nonlinear inequality \(16x \leq x^3\). Express the solution using interval notation and graph the solution set.
57 Skills - Quotient Inequality · Level 3
Solve the nonlinear inequality \(\dfrac{x - 3}{1} \geq 0\). Express the solution using interval notation and graph the solution set.
58 Skills - Quotient Inequality · Level 3
Solve the nonlinear inequality \(\dfrac{2x + 6}{x^2} < 0\). Express the solution using interval notation and graph the solution set.
59 Skills - Quotient Inequality · Level 3
Solve the nonlinear inequality \(\dfrac{4x}{2x + 3} > 2\). Express the solution using interval notation and graph the solution set.
60 Skills - Quotient Inequality · Level 3
Solve the nonlinear inequality \(-2 < \dfrac{x + 1}{x - 3}\). Express the solution using interval notation and graph the solution set.
61 Skills - Quotient Inequality · Level 3
Solve the nonlinear inequality \(\dfrac{2x + 1}{x - 5} \leq 3\). Express the solution using interval notation and graph the solution set.
62 Skills - Quotient Inequality · Level 3
Solve the nonlinear inequality \(\dfrac{3 + x}{3 - x} \geq 1\). Express the solution using interval notation and graph the solution set.
63 Skills - Quotient Inequality · Level 3
Solve the nonlinear inequality \(\dfrac{4}{x} < x\). Express the solution using interval notation and graph the solution set.
64 Skills - Quotient Inequality · Level 3
Solve the nonlinear inequality \(\dfrac{x}{1} > 3x\). Express the solution using interval notation and graph the solution set.
65 Skills - Quotient Inequality · Level 4
Solve the nonlinear inequality \(1 + \dfrac{2}{x + 1} \leq \dfrac{2}{x}\). Express the solution using interval notation and graph the solution set.
66 Skills - Quotient Inequality · Level 4
Solve the nonlinear inequality \(\dfrac{3}{x - 1} - \dfrac{4}{x} \geq 1\). Express the solution using interval notation and graph the solution set.
67 Skills - Quotient Inequality · Level 4
Solve the nonlinear inequality \(\dfrac{6}{x - 1} - \dfrac{6}{x} \geq 1\). Express the solution using interval notation and graph the solution set.
68 Skills - Quotient Inequality · Level 4
Solve the nonlinear inequality \(\dfrac{x}{2} \geq \dfrac{5}{x + 1} + 4\). Express the solution using interval notation and graph the solution set.
69 Skills - Quotient Inequality · Level 4
Solve the nonlinear inequality \(\dfrac{x + 2}{x + 3} < \dfrac{x - 1}{x - 2}\). Express the solution using interval notation and graph the solution set.
70 Skills - Quotient Inequality · Level 4
Solve the nonlinear inequality \(\dfrac{1}{x + 1} + \dfrac{1}{x + 2} \leq 0\). Express the solution using interval notation and graph the solution set.
71 Skills - Polynomial Inequality · Level 3
Solve the nonlinear inequality \(x^4 > x^2\). Express the solution using interval notation and graph the solution set.
72 Skills - Absolute Value Inequality · Level 1
Solve the absolute value inequality \(|x| \leq 4\). Express the answer using interval notation and graph the solution set.
73 Skills - Absolute Value Inequality · Level 1
Solve the absolute value inequality \(|3x| < 15\). Express the answer using interval notation and graph the solution set.
74 Skills - Absolute Value Inequality · Level 1
Solve the absolute value inequality \(|2x| > 7\). Express the answer using interval notation and graph the solution set.
75 Skills - Absolute Value Inequality · Level 1
Solve the absolute value inequality \(\dfrac{1}{2}|x| \geq 1\). Express the answer using interval notation and graph the solution set.
76 Skills - Absolute Value Inequality · Level 2
Solve the absolute value inequality \(|x - 5| \leq 3\). Express the answer using interval notation and graph the solution set.
77 Skills - Absolute Value Inequality · Level 2
Solve the absolute value inequality \(|x + 1| \geq 1\). Express the answer using interval notation and graph the solution set.
78 Skills - Absolute Value Inequality · Level 2
Solve the absolute value inequality \(|2x - 3| \leq 0.4\). Express the answer using interval notation and graph the solution set.
79 Skills - Absolute Value Inequality · Level 2
Solve the absolute value inequality \(|5x - 2| < 6\). Express the answer using interval notation and graph the solution set.
80 Skills - Absolute Value Inequality · Level 2
Solve the absolute value inequality \(|3x - 2| \geq 5\). Express the answer using interval notation and graph the solution set.
81 Skills - Absolute Value Inequality · Level 2
Solve the absolute value inequality \(|8x + 3| > 12\). Express the answer using interval notation and graph the solution set.
82 Skills - Absolute Value Inequality · Level 2
Solve the absolute value inequality \(|\dfrac{x - 2}{3}| < 2\). Express the answer using interval notation and graph the solution set.
83 Skills - Absolute Value Inequality · Level 2
Solve the absolute value inequality \(|\dfrac{x + 1}{2}| \geq 4\). Express the answer using interval notation and graph the solution set.
84 Skills - Absolute Value Inequality · Level 2
Solve the absolute value inequality \(|x + 6| < 0.001\). Express the answer using interval notation and graph the solution set.
85 Skills - Absolute Value Inequality · Level 3
Solve the absolute value inequality \(3 - |2x + 4| \leq 1\). Express the answer using interval notation and graph the solution set.
86 Skills - Absolute Value Inequality · Level 3
Solve the absolute value inequality \(8 - |2x - 1| \geq 6\). Express the answer using interval notation and graph the solution set.
87 Skills - Absolute Value Inequality · Level 3
Solve the absolute value inequality \(7 |x + 2| + 5 > 4\). Express the answer using interval notation and graph the solution set.
88 Skills - Phrase to Absolute Value Inequality · Level 1
Express the phrase as an inequality involving an absolute value: All real numbers \(x\) less than 3 units from 0.
89 Absolute Value Inequalities · Level 2
Find an inequality involving an absolute value that describes the set: all real numbers \(x\) more than 2 units from 0.
90 Absolute Value Inequalities · Level 2
Find an inequality involving an absolute value that describes the set: all real numbers \(x\) at least 5 units from 7.
91 Absolute Value Inequalities · Level 2
Find an inequality involving an absolute value that describes the set: all real numbers \(x\) at most 4 units from 2.
92 Domain of Radical Expressions · Level 2
Determine the values of the variable for which the expression \(\sqrt{16 - 9 x^2}\) is defined as a real number.
93 Domain of Radical Expressions · Level 3
Determine the values of the variable for which the expression \(\sqrt{3 x^2 - 5 x + 2}\) is defined as a real number.
94 Domain of Radical Expressions · Level 3
Determine the values of the variable for which the expression \(\left(\dfrac{1}{x^2 - 5 x - 14}\right)^{\dfrac{1}{2}}\) is defined as a real number.
95 Domain of Radical Expressions · Level 3
Determine the values of the variable for which the expression \(\sqrt[4]{\dfrac{1 - x}{2 + x}}\) is defined as a real number.
96 Solving Inequalities with Constants · Level 3
Solve each inequality for \(x\), assuming that \(a\), \(b\), and \(c\) are positive constants. (a) \(a(b x - c) \geq b c\). (b) \(a \leq b x + c < 2 a\).
97 Inequality Proof · Level 4
Suppose that \(a\), \(b\), \(c\), and \(d\) are positive numbers such that \(\dfrac{a}{b} < \dfrac{c}{d}\). Show that \(\dfrac{a}{b} < \dfrac{a + c}{b + d} < \dfrac{c}{d}\).
98 Application - Temperature · Level 2
Temperature Scales. Use the relationship \(F = \dfrac{9}{5} C + 32\) between Celsius and Fahrenheit to find the interval on the Fahrenheit scale corresponding to the temperature range \(20 \leq C \leq 30\).
99 Application - Temperature · Level 2
Temperature Scales. What interval on the Celsius scale corresponds to the temperature range \(50 \leq F \leq 95\)?
100 Application - Cost Comparison · Level 3
Car Rental Cost. A car rental company offers two plans for renting a car. Plan A: \$30 per day and 10¢ per mile. Plan B: \$50 per day with free unlimited mileage. For what range of miles will Plan B save you money?
101 Application - Cost Comparison · Level 3
Long-Distance Cost. A telephone company offers two long-distance plans. Plan A: \$25 per month and 5¢ per minute. Plan B: \$5 per month and 12¢ per minute. For how many minutes of long-distance calls would Plan B be financially advantageous?
102 Application - Linear Cost · Level 2
Driving Cost. The annual cost of driving a certain new car is given by \(C = 0.35 m + 2200\), where \(m\) is miles driven per year and \(C\) is the cost in dollars. Jane budgets between \$6400 and \$7100 for next year's driving costs. What is the corresponding range of miles that she can drive?
103 Application - Linear Model · Level 3
Air Temperature. As dry air moves upward, it expands and cools at a rate of about 1°C for each 100-meter rise, up to about 12 km. (a) If the ground temperature is 20°C, write a formula for the temperature at height \(h\) (in meters). (b) What range of temperatures can be expected if a plane takes off and reaches a maximum height of 5 km?
104 Application - Linear Model · Level 3
Airline Ticket Price. A charter airline finds that on its Saturday flights from Philadelphia to London all 120 seats will be sold if the ticket price is \$200. However, for each \$3 increase in ticket price, the number of seats sold decreases by 1. (a) Find a formula for the number of seats sold \(N\) if the ticket price is \(P\) dollars. (b) Over a certain period the number of seats sold for this flight ranged between 90 and 115. What was the corresponding range of ticket prices?
105 Application - Tolerance · Level 2
Accuracy of a Scale. A coffee merchant sells a customer 3 lb of Hawaiian Kona at \$6.50 per pound. The merchant's scale is accurate to within \(\pm 0.03\) lb. By how much could the customer have been overcharged or undercharged because of possible inaccuracy in the scale?
106 Application - Inverse Square · Level 3
Gravity. The gravitational force \(F\) exerted by the earth on an object having a mass of 100 kg is given by \(F = \dfrac{4000000}{d^2}\), where \(d\) is the distance (in km) of the object from the center of the earth, and \(F\) is measured in newtons (N). For what distances will the gravitational force exerted by the earth on this object be between 0.0004 N and 0.01 N?
107 Application - Inverse Square · Level 3
Bonfire Temperature. In the vicinity of a bonfire the temperature \(T\) in °C at a distance of \(x\) meters from the center of the fire was given by \(T = \dfrac{600000}{x^2 + 300}\). At what range of distances from the fire's center was the temperature less than 500°C?
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108 Application - Quadratic Inequality · Level 3
Falling Ball. Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 128 ft high, then its height \(h\) above the ground \(t\) seconds later will be \(h = 128 + 16 t - 16 t^2\). During what time interval will the ball be at least 32 ft above the ground?
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109 Application - Quadratic Inequality · Level 3
Gas Mileage. The gas mileage \(g\) (in mi/gal) for a particular vehicle, driven at \(v\) mi/h, is given by \(g = 10 + 0.9 v - 0.01 v^2\), as long as \(v\) is between 10 mi/h and 75 mi/h. For what range of speeds is the vehicle's mileage 30 mi/gal or better?
110 Application - Quadratic Inequality · Level 3
Stopping Distance. For a certain model of car the distance \(d\) required to stop the vehicle if it is traveling at \(v\) mi/h is given by \(d = v + \dfrac{v^2}{20}\), where \(d\) is measured in feet. Kerry wants her stopping distance not to exceed 240 ft. At what range of speeds can she travel?
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111 Application - Quadratic Inequality · Level 4
Manufacturer's Profit. If a manufacturer sells \(x\) units of a certain product, revenue \(R\) and cost \(C\) (in dollars) are given by \(R = 20 x\) and \(C = 2000 + 8 x + 0.0025 x^2\). Use the fact that profit equals revenue minus cost to determine how many units the manufacturer should sell to enjoy a profit of at least \$2400.
112 Application - Geometry/Optimization · Level 3
Fencing a Garden. A determined gardener has 120 ft of deer-resistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area enclosed to be at least 800 ft\(^2\). What range of values is possible for the length of her garden?
113 Application - Tolerance · Level 2
Thickness of a Laminate. A company manufactures industrial laminates (thin nylon-based sheets) of thickness 0.020 in, with a tolerance of 0.003 in. (a) Find an inequality involving absolute values that describes the range of possible thicknesses \(t\) for the laminate. (b) Solve the inequality you found in part (a).
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114 Application - Absolute Value Inequality · Level 3
Range of Height. The average height of adult males is 68.2 in, and 95% of adult males have height \(h\) that satisfies the inequality \(|\dfrac{h - 68.2}{2.9}| \leq 2\). Solve the inequality to find the range of heights.
115 Discovery - Powers and Order · Level 4
Do Powers Preserve Order? If \(a < b\), is \(a^2 < b^2\)? (Check both positive and negative values for \(a\) and \(b\).) If \(a < b\), is \(a^3 < b^3\)? On the basis of your observations, state a general rule about the relationship between \(a^n\) and \(b^n\) when \(a < b\) and \(n\) is a positive integer.
116 Discovery - Inequality Errors · Level 4
What's Wrong Here? It is tempting to try to solve an inequality like an equation. For instance, we might try to solve \(1 < \dfrac{3}{x}\) by multiplying both sides by \(x\), to get \(x < 3\), so the solution would be \((-\infty, 3)\). But that's wrong; for example, \(x = -1\) lies in this interval but does not satisfy the original inequality. Explain why this method doesn't work (think about the sign of \(x\)). Then solve the inequality correctly.
117 Discovery - Geometric Interpretation · Level 4
Using Distances to Solve Absolute Value Inequalities. Recall that \(|a - b|\) is the distance between \(a\) and \(b\) on the number line. For any number \(x\), what do \(|x - 1|\) and \(|x - 3|\) represent? Use this interpretation to solve the inequality \(|x - 1| < |x - 3|\) geometrically. In general, if \(a < b\), what is the solution of the inequality \(|x - a| < |x - b|\)?
118 Example - Linear Inequality · Level 2
**Solving a Linear Inequality.** Solve the inequality \(3 x < 9 x + 4\) and sketch the solution set.
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119 Example - Simultaneous Inequalities · Level 2
**Solving a Pair of Simultaneous Inequalities.** Solve the inequalities \(4 \leq 3 x - 2 < 13\).
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120 Example - Quadratic Inequality · Level 3
**Solving a Quadratic Inequality.** Solve the inequality \(x^2 \leq 5 x - 6\).
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121 Example - Solving an Inequality with Repeated Factors · Level 3
Solve the inequality \(x(x-1)^2(x-3) < 0\).
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122 Example - Solving an Inequality Involving a Quotient · Level 3
Solve the inequality \(\dfrac{1+x}{1-x} \geq 1\).
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123 Example - Solving an Absolute Value Inequality · Level 2
Solve the inequality \(|x - 5| < 2\).
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124 Example - Solving an Absolute Value Inequality · Level 2
Solve the inequality \(|3x + 2| \geq 4\).
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125 Example - Modeling with Inequalities (Carnival Tickets) · Level 2
A carnival has two plans for tickets. Plan A: \$5 entrance fee and 25¢ each ride. Plan B: \$2 entrance fee and 50¢ each ride. How many rides would you have to take for Plan A to be less expensive than Plan B?
126 Example - Relationship Between Fahrenheit and Celsius Scales · Level 2
The instructions on a bottle of medicine indicate that the bottle should be stored at a temperature between \(5^{\circ}\) C and \(30^{\circ}\) C. What range of temperatures does this correspond to on the Fahrenheit scale?

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