Section 2.7 Linear Inequalities in One Variable 171 4b. -4x ≤ 4 -4x -4 ≥ 4 -4 x≥-1 Divide each side by -4 and reverse the inequality symbol. Simplify. The graph consists of all values greater than or equal to -1; that is, numbers to the right of -1 and including -1. –5 –4 –3 –2 –1 0 1 2 3 4 5 Interval notation: -1, -∞) Set-builder notation: Exux≥-1F 4c. 3y - 7 > 2 3y - 7 + 7 > 2 + 7 3y > 9 3y 3 > 9 3 y > 3 The graph consists of all values greater than 3, or to the right of 3, but not including 3. –5 –4 –3 –2 –1 0 1 2 3 4 5 Interval notation: (3, ∞) Set-builder notation: Eyuy > 3F 4d. 3(2a + 1) - a ≥ 2a - 7 6a + 3 - a ≥ 2a - 7 Apply the distributive property. 5a + 3 ≥ 2a - 7 Combine like terms. 5a + 3 - 2a ≥ 2a - 7 -2a Subtract 2a from each side. 3a + 3 ≥ -7 Simplify. 3a + 3 - 3 ≥ -7 - 3 Subtract 3 from each side. 3a ≥ -10 Simplify. 3a 3 ≥ -10 3 Divide each side by 3. a≥- 10 3 Simplify. The graph consists of all numbers to the right of - 10 3 , including - 10 3 . –5 –4 –3 –2 –1 0 1 2 3 4 5 Interval notation: c- 10 3 , ∞b Set-builder notation: e a` a≥- 10 3 f Add 7 to each side. Simplify. Divide each side by 3. Simplify.
hendricks_beginning_algebra_1e_ch1_3
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