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Compound Inequalities Objective: To solve conjunctions and disjunctions

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Conjunction A sentence formed by joining two sentences with the word and. x > -3 and x < 4 in order for a value of x to make the statement true both conditions must be satisfied. -34

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Disjunction Formed by joining two sentences with the word or A solution only has to satisfy one of the conditions to be true x > 2 states that x > 2 or x = 2, notice that the dot is shaded in to show equality. x > 3 or x <

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Solving Inequalities With Disjunction 2x + 3 < 7 or -4x < -16 2x + 3 – 3 < 7 – 3 2x < 4 2x/2 < 4/2 x < 2 -4x < x/-4 > -16/-4 x > 4 x 4 42

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Solving Inequalities With Conjunction 4 < 2(x – 1) 4 < 2x – 2 distribute < 2x – < 2x 6/2 < 2x/2 3 < x x > 3 2(x – 1) < 8 2x – 2 < 8 distribute 2x – < x < 10 2x/2 < 10/2 x < 5 4 < 2(x – 1) < 8 4 < 2(x – 1) and 2(x – 1) < 8 x > 3 and x < 5 53

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Alternative Solution For Conjunction 4 < 2(x – 1) < 8 4 < 2x – 2 < 8 distribute < 2x – < < 2x < 10 6/2 < 2x/2 < 10/2 3 < x < 5 53

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Try These! Solve and Graph each Compound Inequality -2 < 3x + 1 or 3x < -9 6 < 3x + 6 < 12 6 > 2x > -8 2x – 1 > 3 or x – 2 < 3 2x x > -1 or x < -3 Click for solution 0 < x < 2 Click for solution -4 < x < 3 Click for solution All Real Numbers Click for solution Ø End show

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-2 < 3x + 1 or 3x < – 1 < 3x + 1 – 1 -3 < 3x -3/3 < 3x/3 -1 < x x > -1 3x/3 < -9/3 x < -3 x > -1 or x < -3 Back to Try These!

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6 < 3x + 6 < 12 6 – 6 < 3x + 6 – 6 < 12 – 6 0 < 3x < 6 0/3 < 3x/3 < 6/3 0 < x < 2 Back to Try These!

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6 > 2x > -8 6/2 > 2x/2 > -8/2 3 > x > < x < 3 Back to Try These!

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2x – 1 > 3 or x – 2 < 3 2x – > x > 4 2x/2 > 4/2 x > 2 x – < x < 5 x > 2 or x < 5 52 Back to Try These!

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2x x + 3 – 3 < 3 – 3 2x < 0 2x/2 < 0/2 x < 0 x – > x > 5 Because there is no value for x that satisfies x 5 simultaneously there is no solution for the inequality Back to Try These!

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