Math 095 - Intermediate Algebra - Prairie State College

Objective 6: Find unions and intersections of intervals. Sketch the graph of an interval.
Convert between interval notation and inequality notation.
15. Find the union and the intersection of the intervals (−∞, 6] and (−3, ∞).
(a) union: (−3, 6), intersection: (−∞, ∞)
(b) union: (−∞, ∞), intersection: (−3, 6]
(c) union: (−∞, −3), intersection: [6, ∞)
(d) union: (−∞, ∞), intersection: (−3, 6)
16. Which one of the following intervals is described by the inequality −2 ≤ x < 17
(a) (−2, 17]
(b) (−∞, −2] ∪ (17, ∞)
(c) [−2, 17)
(d) (−∞, −2] ∩ (17, ∞)
17. Sketch the graph of the interval described by the inequality 5 < x ≤ 12.
(a) ✛ ❢ ✈
5 12
(b) ✛ ✈ ❢
5 12
(c) ✛ ✈ ✈
5 12
(d) ✛ ❢ ❢
5 12
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Objective 7: Solve compound linear inequalities in one variable. Solve application problems
that require setting up and solving linear inequalities in one variable.
18. Solve the following compound inequality. Write your solution in interval notation.
(a) (−2, 1]
(b) (−1, 2]
(c) There is no solution.
(d) All real numbers are solutions.
−11 < 5x − 1 ≤ 4
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