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Solving Compound Inequalities Tutorial

Understand compound inequalities with AND and OR statements through examples, graphs, and solutions. Practice problems and explanations provided. Improve your math skills!

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Solving Compound Inequalities Tutorial

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  1. Do Now 10/7/19 • Copy HW in your planner. • Text p. 85, #3-6, 8-24 evens Find 20% of $350. Find 15% of $70.

  2. Using your Big Ideas Student Journal, complete Explorations 1 & 2 for Section 2.5. Then on page 50, make a Venn diagram comparing and contrasting cats & dogs. You can work with your 4:00 partners.

  3. Learning Goal Learning Target SWBAT write, graph, and solve linear, compound, and absolute value inequalities • SWBAT write, graph, and solve compound inequalities

  4. Section 2.5“Solving Compound Inequalities” COMPOUND INEQUALITY – consists of two separate inequalities joined by AND or OR.

  5. “AND” Compound Inequalities • The graph of a compound inequality with AND is the INTERSECTION of the graphs of the inequalities. Graph x > -2 -1 0 1 2 3 -2 Graph x ≤ 1 -2 -1 0 1 2 3 Graph of x ≤ 1 and x > -2 -2 -1 0 1 2 3

  6. “OR” Compound Inequalities • The graph of a compound inequality with OR is the UNION of the graphs of the inequalities. Graph x > 2 -1 0 1 2 3 -2 Graph x ≤ -1 -2 -1 0 1 2 3 Graph of x ≤ -1 or x > 2 -2 -1 0 1 2 3

  7. Graph each compound inequality 5 < y ≤ 9 5 6 7 8 9 10 4 h > 1 or h ≤ -3 -4 -3 -2 -1 0 1 2

  8. Graph each compound inequality y ≤ 16 or y > 20 15 16 17 18 19 20 14 h > -3 and h ≤ 0 -4 -3 -2 -1 0 1 2

  9. All real numbers that are greater than –2and less than 3. Graph: All real numbers that are less than 0or greater than or equal to 2. Graph: Translate the verbal phrase into an inequality. Then graph the inequality. Inequality: – 2 < x < 3 Inequality: x < 0 or x ≥ 2

  10. Solve a Compound Inequality with AND Solve 2 < x + 5 < 9.Graph your solution. Separate the compound inequality into two inequalities. Then solve each inequality separately. 2 < x + 5 x + 5 < 9 and Write two inequalities. 2 – 5< x + 5 – 5 and x + 5 – 5< 9 – 5 Subtract 5 from each side. and x < 4 -3 < x Simplify. The compound inequality can be written as – 3 < x < 4.

  11. Graph: – 3 – 2 – 1 0 1 2 3 4 5 Solve a Compound Inequality with AND Solve –7 < x – 5 < -1.Graph your solution. Separate the compound inequality into two inequalities. Then solve each inequality separately. –7 < x – 5 x – 5 < -1 and Write two inequalities. x – 5 + 5< -1 + 5 –7+ 5< x –5+ 5 and Add 5 to each side. and –2 < x x < 4 Simplify. The compound inequality can be written as – 2 < x < 4.

  12. The solutions are all real numbers less than 3or greater than 6. Solve a Compound Inequality with OR Solve 2x + 3 < 9 or3x – 6 > 12. Graph your solution. Solve the two inequalities separately. or 2x + 3 < 9 3x – 6 > 12 Write original inequality. or 3x – 6 + 6> 12 + 6 2x + 3 – 3< 9 – 3 Addition or Subtraction property of inequality or 2x < 6 3x > 18 Simplify. or x > 6 x < 3 Simplify.

  13. Solve a Compound Inequality with OR Solve Graph your solution. 3h + 1< – 5 or 2h – 5 > 7 Solve the two inequalities separately. 3h + 1< – 5 or 2h – 5 > 7 Write two inequalities. 3h + 1 – 1< – 5 – 1 or 2h – 5 + 5 > 7 + 5 Addition & Subtraction property inequalities. or 3h < – 6 2h > 12 or h > 6 Simplify. h < – 2 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7

  14. Exit Ticket GoFormative.com • Solve and graph the inequality • -12 < ½(4x + 16) < 18 • “How Are You Doing?” Give yourself a rating on today’s lesson (Section 2.5 Compound Inequalities) – 4, 3, 2, or 1. Write your rating in the circle in the upper right hand corner.

  15. What Did You Learn Today? “OR” statement “AND” statement

  16. Homework • Text p. 85, #3-6, 8-24 evens

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