168 Chapter 2 Linear Equations and Inequalities in One Variable Positive and negative infinity are always written with parentheses because they don’t represent a specific number. Two examples are shown next. –5 –4 –3 –2 –1 0 1 2 3 4 5 Left –∞ Right 4 (– ∞, 4 –5 –4 –3 –2 –1 0 1 2 3 4 5 Left –2 Right ∞ (–2, ∞) �� ������������������������ ������������������ Complete the table by graphing each inequality and writing the interval notation that corresponds to the solution set. Inequality Graph Interval Notation 2a. x > 3 0 1 2 3 4 5 6 7 8 9 10 (3, ∞) 2b. x ≤ 1.5 –5 –4 –3 –2 –1 0 1 2 3 4 5 (-∞, 1.5 2c. 1 2 < x –5 –4 –3 –2 –1 0 1 2 3 4 5 a1 2 , ∞b 2d. -2 < x ≤ 5 –5 –4 –3 –2 –1 0 1 2 3 4 5 (-2, 5 Student Check 2 Graph each inequality and express the solution set in interval notation. a. x > -2 b. x ≤ -4.2 c. 5 3 > x d. -4 ≤ x < 2 Set-Builder Notation Set-builder notation is another way to represent the solution set of an inequality. Setbuilder notation was briefly discussed in Chapter 1. Set-builder notation is used to state conditions that the solutions must satisfy. An example is shown. Set-builder Notation Verbal Statement Exux ≤ 4F The set of all x such that x is less than or equal to 4. �� ������������������������ �������������������� Graph each inequality and express the solution set in set-builder notation. Inequality Graph Set-Builder Notation 3a. x > 3 0 1 2 3 4 5 6 7 8 9 10 Exux > 3F 3b. x ≤ 1.5 –5 –4 –3 –2 –1 0 1 2 3 4 5 Exux ≤ 1.5F 3c. 1 2 < x –5 –4 –3 –2 –1 0 1 2 3 4 5 e x` x > 1 2 f 3d. -2 < x ≤ 5 –5 –4 –3 –2 –1 0 1 2 3 4 5 Exu-2 < x ≤ 5F Objective 3 ▶ Write the solution set of an inequality in set-builder notation.
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