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1.4 Solving Inequalities

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.

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1.4 Solving Inequalities

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  1. 1.4 Solving Inequalities

  2. 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

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

  4. Solving Inequalities and Graphing -1 0 1 2 Interval Notation (-∞, 1/5 ]

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

  6. 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 !

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

  8. COMPOUND INEQUALITIES“AND” Case -7 0 6

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

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

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