6.3 Compound Inequalities

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Presentation transcript:

6.3 Compound Inequalities Objective: How to solve and graph compound inequalities How to model a real life situation with a compound inequality

Learn to Read… a< x <b Read: x is between a and b a< x < b Read: x is between a & b inclusive

Graph: 1< x < 5 Read as: ? x is between 1 and 5 1 2 3 4 5 6 7

x greater than 2 or x less than -1 Write the inequality x greater than 2 or x less than -1 x < -1 x > 2 Graph: -2 -1 1 2 3 *Remember: (closed circle) • when the number is included!

Solve Compound Inequalities and Graph: Solve like an equation, but now you have three parts! -9 < 6x + 3 ≤ 39 Subtract 3 from all three parts. -3 -3 -3 -12 < 6x ≤ 36 Divide each part by 6. 6 6 6 -2 < x ≤ 6 GRAPH: -3 -2 -1 1 2 3 4 5 6 7

Write the inequality, solve and then graph: Eight plus two times a number is less than six. 8 + 2x < 6 -8 -8 2x < -2 x < -1 -2 -1 1 2 3

Write the inequality, solve and then graph: Eight times a number x plus 4 is between -4 and 20. -4< 8x + 4 < 20 -4 -4 -4 -8 < 8x < 16 -1 < x < 2 -2 -1 1 2 3 The numbers should be displayed least to greatest Example you would not write 2 > x > -1

Practice: Graph 1. x > 4 or x < -2 2. -2 < x < 3 Solve -3 -2 -1 1 2 3 4 5 -2 -1 1 2 3 Solve 2 + x > 3 3 < 2 - x < 5 Same thing as.. But # line order 5. Write an inequality for the following graph 2 3 4 5 6 7 8 9 10 4≤ x ≤ 8