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1.4 Solving Inequalities 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 Solving Inequalities and Graphing 7x – 5 < 6x + 4 x–5<4 x<9 -5 0 9 Interval Notation (-∞, 9) Solving Inequalities and Graphing x2 x 9 9x x 2 10x 2 1 x 5 -1 0 1 2 Interval Notation (-∞, 1/5 ] Solving Inequalities and Graphing 4(x – 3) < 2(2x – 5) 4x – 12 < 4x – 10 – 12 < – 10 All reals Interval Notation (-∞, ∞) Ex- special case 2 • • • • • • • 2(3x + 5) > 6(x – 1) + 17 6x + 10 > 6x – 6 + 17 6x + 10 > 6x – 6 + 17 6x + 10 > 6x + 11 10 > 11 NO SOLUTION - no value of x works ! COMPOUND INEQUALITIES “AND” Case 13< 2x + 7< 17 x<5 x>3 3<x<5 13 < 2x+7 2x+7<17 Interval Notation (3, 5) COMPOUND INEQUALITIES “AND” Case 20 3x 1 19 20 3x 1 x 7 3x 1 19 x6 7 x 6 -7 0 6 COMPOUND INEQUALITIES “OR” case y – 2> -3 or y + 4 < -3 y > -1 y < -7 -7 -5 Interval Notation (- ∞,-7) and (-1,∞) -3 -1 COMPOUND INEQUALITIES “OR” case 3( x 1) 4 OR 3x 3 4 3x 1 1 x 3 2( x 3) 4 2x 6 4 2x 10 x 5 Interval Notation: All real numbers