Today’s Date: 9/13/11 2.1 Solving Inequalities in 1 Variable & 2.2 Solving Combined Inequalities.

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Presentation transcript:

Today’s Date: 9/13/ Solving Inequalities in 1 Variable & 2.2 Solving Combined Inequalities

Solving Inequalities Ex 1) y + 4 < 3 – 4 – 4 y < – 1 treat like = Graph –1 ≥ or ≤ closed circle open circle

Ex 2) Solve & Graph: –12 ≥ – 4y When multiply or divide by (–) #, flip inequality sign –12 ≥ –4y –4 –4 3 ≤ y y ≥ 3 3 flip!! write variable on left Graph closed circle

Ex 3) Solve & Graph: 5x + 17 < 2 5x + 17 < 2 –17 –17 5x < – x < –3 Ex 4) 4x + 3(2 – 3x) < 5(2 – x) 4x + 6 – 9x < 10 – 5x –5x + 6 < 10 – 5x 6 < 10 –3 always true!! flip? NO! All Real #s

2.2 Solving Combined Inequalities Ex 5) Solve & Graph x ≥ –1 AND x < 3 (AND is the overlap) –1 3 ≥ or ≤ closed circle open circle This is the same as: –1 ≤ x < 3 You just split it up as x ≥ –1 AND x < 3

Ex 6) Graph: x > 2 OR x ≤ 0 Graph OR on # line Ex 7) Solve & Graph: 3 < 2x + 5 ≤ 15 2x + 5 > 3 AND 2x + 5 ≤ –1 split into AND statement 2x > –2 x > –1 2x ≤ 10 x ≤ 5 careful!!

–2y ≤ –6 y ≥ 3 TOO Ex 8) Solve & Graph 7 – 2y ≤ 1 OR 3y + 10 < 4 – y 3 –3/2 4y + 10 < 4 4y < –6 y < –3/2 flip!!

TOO Ex 9) Solve & Graph 3x – 1 > –28 AND 2x + 7 > 19 (AND is the overlap) –9 6 3x > –27 x > –9 2x > 12 x > 6 AND Answer: x > 6

Homework #201 Pg – 23 odd Pg – 31 odd