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Solve each compound inequality. Write the solutio…

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 93 Problem 94 Problem 95 Problem 96 Problem 97 Problem 98 Problem 99 Problem 100 Problem 101 Problem 102 Problem 103 Problem 104 Problem 105 Problem 106 Problem 107 Problem 108 Problem 109 Problem 110 Problem 111 Problem 112 Problem 113 Problem 114 Problem 115 Problem 116 Problem 117 Problem 118 Problem 119 Problem 120 Problem 121 Problem 122 Problem 123 Problem 124

Problem 59 Hard Difficulty

Solve each compound inequality. Write the solution set in interval notation and graph.
$$
3 \leq 2 x-1<5
$$

Answer

$$[2,3)$$

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Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 7

Solving Inequalities

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Video Transcript

solved the compound inequality, right? The solution. Set an interval notation and graph it. We have the compound inequality. Three is less than or equal to two X minus. One is less than five. To solve the compound inequality, we will use properties of inequality to isolate the variable by itself as the middle part of the inequality. Right now we have two X minus one as the middle part of the inequality. We need to isolate X by using inverse operations, and we're going to start first by undoing the subtraction. Add one to all parts of the inequality this gives us four is less than or equal to two. X is less than six excess still not isolated, So we need to undo the product using division to get X by itself, divide by two. To keep the inequality true, we need to divide all parts by two. This gives us a new inequality. That he's equivalent as two is less than or equal to X is less than three. This compound inequality can be shown on a number. Line two is less than or equal to X is less than three indicates that X is greater than or equal to two. So we're going to start at two with a closed circle to include the value. But X is also less than three. So at three, we haven't open circle because three is not included in the solution. Set includes all the values in between these two end points an interval notation. We will open with a bracket at two to include the value to and close with a parentheses, e at three because three is not included.

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Alan S. Tussy, R. David Gustafson

Elementary and Intermediate Algebra

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