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8.2 Linear Inequalities

8.2 Linear Inequalities. We will remind ourselves how to solve inequalities and graph on a number line as well as the coordinate plane. Graph. Interval ( a , b ) [ a , b ] [ a , b ) ( a , b ] ( a , ∞) [ a , ∞) (–∞, a ) (–∞, a ]. Inequality a < x < b a ≤ x ≤ b a ≤ x < b

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8.2 Linear Inequalities

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  1. 8.2 Linear Inequalities

  2. We will remind ourselves how to solve inequalities and graph on a number line as well as the coordinate plane Graph Interval (a, b) [a, b] [a, b) (a, b] (a, ∞) [a, ∞) (–∞, a) (–∞, a] Inequality a < x < b a ≤ x ≤ b a ≤ x < b a < x ≤ b x > a x ≥ a x < a x ≤ a a b a b a b a b a a a a

  3. In a compound inequality, two conditions are given - conjunction - disjunction  “and”  the intersection of the sets  “or”  the union of the sets Ex 1) Solve and graph on a number line. Express in interval notation. a) • 6 – 10x < 5 • – 10x < –1 • 3 ≤ 4x – 1 < 7 • 3 ≤ 4x – 1 • 4 ≤ 4x • 1 ≤ x • x ≥ 1 *deal with one part at a time* b) • 4x – 1 < 7 • 4x < 8 • x < 2 2 1 [1, 2)

  4. Ex 1) Solve and graph on a number line. Express in interval notation. c) • 2x – 3 ≥ 2 or 2x – 3 < –4 • 2x ≥ 5 • 2x < –1 Absolute Value: *Remember could mean x = 2 or x = –2 *Hint: ││< # ││> # say “less thAND” say “greatOR” Ex 2) Solve and graph on a number line. Express in interval notation. a) │6 – 4x│ ≤ 2 “and” and 6 – 4x ≥ –2 –4x ≥ –8 x ≤ 2 6 – 4x ≤ 2 –4x ≤ –4 x ≥ 1 2 1 [1, 2]

  5. Ex 2) Solve and graph on a number line. Express in interval notation. b) │2x + 1│ > 3 “or” or 2x + 1 < –3 2x < –4 x < –2 2x + 1 > 3 2x > 2 x > 1 –2 1 (–∞, –2)  (1, ∞) Graphing linear inequalities in two variables in the coordinate plane < or > dotted line ≤ or ≥ solid line y < or y ≤ shade “below” y > or y ≥ shade “above” The two regions the coordinate plane is divided into is called half-plane. The line is the boundary. closed half-plane: solid line open half-plane: dotted line

  6. Ex 3) Graph in the coordinate plane 3x – y > 4 –y > –3x + 4 y < 3x – 4 shade below b) –3 ≤ 2x + y < 6 –3 ≤ 2x + y –y ≤ 2x + 3 y ≥ –2x – 3 shade above do each line 2x + y < 6 y < –2x + 6 shade below

  7. y < –│x + 2│ abs value reflect over x-axis shifted 2 left dotted line shade below

  8. Homework #802 Pg 398 #1, 5, 9, 13, 16, 21, 24, 29, 34, 38, 39, 43, 44

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