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§6.3 – Compound Inequalities

§6.3 – Compound Inequalities. SWBAT graph the solution sets of compound inequalities and solve compound inequalities. OR Values that are solutions to ONE of the inequalities. -5. -5. -4. -4. -3. -3. -2. -2. -1. -1. 0. 0. 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. AND

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§6.3 – Compound Inequalities

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  1. §6.3 – Compound Inequalities SWBAT graph the solution sets of compound inequalities and solve compound inequalities.

  2. OR Values that are solutions to ONE of the inequalities. -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 • AND • Values that are solutions to BOTH inequalities Graphs of Compound Inequalities Graph both inequalities, and the solution is where the graphs overlap. Graph both inequalities, & the solution is everything graphed.

  3. All real numbers that are greater than or equal to -4 and less than 4. -5 -4 -3 -2 -1 0 1 2 3 4 5 Example 1Translate the verbal phrase into an inequality. Then graph the inequality. x  -4 and x < 4 and x < 4 -4  x -4  x < 4

  4. All real numbers that are less than -1 or greater than 2. -5 -4 -3 -2 -1 0 1 2 3 4 5 Example 2Translate the verbal phrase into an inequality. Then graph the inequality. x < -1 or x > 2

  5. -5 -4 -3 -2 -1 0 1 2 3 4 5 Example 3Solve -1 < x + 1  7 Write two inequalities Subtract 1 from each side Simplify Write as a compound ineq. Graph

  6. -10 -8 -6 -4 -2 0 2 4 6 8 10 Example 4Solve 1 < -2x + 3 < 19 Write two inequalities Subtract 3 from each side Simplify Divide each side by -2 ***Flip the inequalities!*** Simplify Write as a compound ineq. Graph

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