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Section 6-4

Section 6-4. Solve Compound Inequalities. Compound Inequality : Two separate inequalities joined by and or or. • The graph of a compound inequality with and is the intersection of the graphs of the inequalities. • The graphs go TOWARDS each other.

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Section 6-4

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  1. Section 6-4 Solve Compound Inequalities

  2. Compound Inequality: Two separate inequalities joined by and or or. • The graph of a compound inequality with and is the intersection of the graphs of the inequalities. • The graphs go TOWARDS each other. • The graph of a compound inequality with or is the union of the graphs of the inequalities. • The graphs go AWAY from each other.

  3. Example 1 Write and graph compound inequalities: a) All real numbers that are greater than or equal to -4 and less than 4. -4 ≤ x < 4 Graph: -8 -6 -4 -2 0 2 4 6

  4. Example 1 Continued Write and graph compound inequalities: b) All real numbers that are less than -1 or greater than 2. x < -1 or x > 2 Graph: -3 -2 -1 0 1 2 3 4

  5. Example 2 Solve a compound inequality with and: 1 < -2x + 3 < 19 -3 - 3 - 3 -2 < -2x < 16 -2 -2 -2 1 > x > -8 -8 < x < 1 Graph: -8 -6 -4 -2 0 2 4 6 Given APOI Simplify Flip inequalities b/c divided by negative! MPOI Simplify

  6. Example 3 Solve each inequality separately. Solve a compound inequality with or: 3x – 2 ≤ -11or 2x + 8 > 16 Graph: -8 -6 -4 -2 0 2 4 6 Given Given +2 +2 - 8 -8 APOI APOI Simplify 3x ≤ -9 2x > 8 Simplify 3 3 2 2 MPOI MPOI Simplify Simplify or x > 4 x ≤ -3

  7. Homework Section 6-4 Pg. 384 – 387 3 – 5 Solve & Prove: 9 – 19 odd Follow Directions: 21

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