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OBJECTIVE

Learn to write, solve, and graph compound inequalities involving real numbers with guided practice examples and solutions.

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OBJECTIVE

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  1. OBJECTIVE • I will write, solve, and graph compound inequalities.

  2. Writing Compound Inequalities Write an inequality that represents the set of numbers and graph the inequality. • All real numbers that are greater than 2 and less than or equal to 7. 2 < x ≤ 7 • All real numbers that are less than -4 or greater than 3. x < -4 or x > 3

  3. Guided Practice • All real numbers less than or equal to 3 or greater than or equal to 5. • All real numbers greater than -1 but less than or equal to 4.

  4. Solving a Compound Inequality with And Solve 8 < 3x + 2 ≤ 14. 8 < 3x + 2 ≤ 14 Original Inequality - 2 - 2 - 2 (Remember: Inverse Operations) 6 < 3x ≤ 12 Subtract 2 from all sides 3 3 3 Divide all sides by 3 2 < x ≤ 4 Simplify Graph

  5. Solving a Compound Inequality with Or Solve 2x + 5 < 9 or x - 4 ≥ 8 2x + 5 < 9 or x - 4 ≥ 8 Original Inequality 2x < 4 or x ≥ 12 Add/Subtract x < 2 or x ≥ 12 Divide Graph

  6. Reversing Both Inequality Symbols Solve -4 < -5 - x < 3. Graph the solution. -4 + 5 < -5 + 5 - x < 3 + 5 Add 5 to all sides 1 < -x < 8 Simplify -8 < x < -1 Multiply all sides by -1 and reverse signs Graph

  7. Guided Practice Solve the inequality and graph the solution. • 3x + 1 < 4 or 2x - 1 > 7 • 12 < x - 2 < 15 • -1 < -x + 3 < 5

  8. Modeling with a Compound Inequality You have a friend Bill who lives three miles from school and another friend Mary who lives two miles from the same school. You wish to estimate the distance that separates their homes. • What is the smallest possible value of d? • What is the largest possible value of d? • Write an inequality that describes the possible values of d.

  9. Independent Practice Solve the inequality and graph the solution. • 4x + 1 < -7 or 8x + 3 > 27 • 4 < 6x + 10 < 28 • -9x + 3 ≤ 30 or -2x + 8 ≥ -4 • -5 ≤ 3x + 1 ≤ 34 • The lowest temperature ever recorded was -128.6ºF at the Soviet station Vostok in Antarctica. The highest temperature ever recorded was 136ºF at Azizia, Libya. Write a compound inequality whose solution includes all of the other temperatures T ever recorded.

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