Solving Compound Inequalities

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Presentation transcript:

Solving Compound Inequalities NOTES 1.4 Solving Compound Inequalities

Graphing Inequalities Open dot: > or < ( , ) Closed dot: ≥ or ≤ [ , ] Which direction to shade the graph? If x is on left, shade in the direction of arrow If x is on the right, shade opposite the arrow

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

Solving Inequalities and Graphing 4(x – 3) < 2(2x – 5) 4x – 12 < 4x – 10 – 12 < – 10 (true) All real #’s Interval Notation (-∞, ∞)

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

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)

COMPOUND INEQUALITIES “AND” Case Interval Notation [7, 6) -7 6

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

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

COMPOUND INEQUALITIES “AND” Case -7 6 Interval Notation [-7, 6)