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Published byMarianna Rogers Modified over 6 years ago

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1.4 Solving Inequalities

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Review: Graphing Inequalities Open dot:> or < Closed dot:> or < Which direction to shade the graph? –Let the arrow point the way Note: the variable has to be on the left for this trick to work

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Solving Inequalities and Graphing 7x – 5 < 6x + 4 x – 5 < 4 x < 9 0-59 Interval Notation (- ∞, 9)

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Solving Inequalities and Graphing 012 Interval Notation (- ∞, 1/5 ]

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Solving Inequalities and Graphing 4(x – 3) < 2(2x – 5) 4x – 12 < 4x – 10 – 12 < – 10 All reals Interval Notation (- ∞, ∞ )

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Ex- special case 2 2(3x + 5) > 6(x – 1) + 17 6x + 10 > 6x – 6 + 17 6x + 10 > 6x + 11 10 > 11 NO SOLUTION - no value of x works !

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COMPOUND INEQUALITIES “AND” Case 13< 2x + 7< 17 13 < 2x+7 2x+7<17 3 < x < 5 Interval Notation (3, 5 ) x < 5 x > 3

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COMPOUND INEQUALITIES “AND” Case -706

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COMPOUND INEQUALITIES “OR” case y – 2> -3 or y + 4 < -3 y > -1 y < -7 -5-7-3 Interval Notation (- ∞,- 7) and (-1,∞ )

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COMPOUND INEQUALITIES “OR” case OR Interval Notation: All real numbers

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