Objectives: 1.Graph (and write) inequalities on a number line. 2.Solve and graph one-variable inequalities. (Linear) 3.Solve and graph compound inequalities.

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Presentation transcript:

Objectives: 1.Graph (and write) inequalities on a number line. 2.Solve and graph one-variable inequalities. (Linear) 3.Solve and graph compound inequalities. (Linear) 4.Solve and graph ABSOLUTE VALUE inequalities. Warm Up: Solve the following Inequalities 1.-3(2x - 7) > > -3(2x - 7)

I. Solving Compound Inequalities “AND” Example 1 : -2 < x + 2 ≤ 4 x + 2 ≤ x ≤ 2 -2 < x < x -4 < x ≤ < x + 2 ≤ < x ≤ 2 Test Value:-2 < ≤ 4 -2 < -3 ≤ 4 Test Value:-2 < ≤ 4 -2 < 2 ≤ 4 FALSETRUEFALSE Test Value:-2 < ≤ 4 -2 < 6 ≤ 4

Example 2: -3 ≤ 2x + 1 ≤ ≤ 2x ≤ ≤ x ≤ I. Solving Compound Inequalities “AND” Test Value:-3 ≤ 2(-3) + 1 ≤ 5 -3 ≤ -5 ≤ 5 Test Value:-3 ≤ 2(0) + 1 ≤ 5 -3 ≤ 1 ≤ 5 Test Value:-3 ≤ 2(3) + 1 ≤ 5 -3 ≤ 7 ≤ 5 FALSETRUEFALSE

Example 3: -9 ≤ -3(2x + 7) ≤ ≤ -6x - 21 ≤ ≤ -6x ≤ ≥ x ≥ I. Solving Compound Inequalities “AND” Test Value:-9 ≤ -3(2(-7) + 7) ≤ ≤ 21 ≤ 15 Test Value: -9 ≤ -3(2(-5) + 7) ≤ ≤ 9 ≤ ≤ -3(2(0) + 7) ≤ ≤ -21 ≤ 15 FALSE TRUE

Example 5: 3x x + 13 < x < -9 3 x < -3 2x - 5 > x > 12 2 x > 6 x II. Solving Compound Inequalities “OR” Test Value:3(-5) Test Value: TRUE FALSE 3(0) (7)

Example 6: 2(2x + 3) ≤ 2 or -7(3x – 5) < -7 2(2x + 3) ≤ 2 4x + 6 ≤ x ≤ -4 4 x ≤ -1 -7(3x - 5) < x + 35 < x < x > 2 x ≤ -1 or x > II. Solving Compound Inequalities “OR” TRUE FALSE Test Value:2(2(-2) + 3) ≤ 2 or -7(3(-2) – 5) < ≤ 2 or 77 < -7 Test Value: 2(2(0) + 3) ≤ 2 or -7(3(0) – 5) < -7 6 ≤ 2 or 35 < -7 2(2(3) + 3) ≤ 2 or -7(3(3) – 5) < ≤ 2 or -28 < -7