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Solving Inequalities by Multiplication & Division

Solving Inequalities by Multiplication & Division. Solving Inequalities by Multiplication & Division. Objective : 7.5.03 Essential Question : How can we use inverse operations to solve one step multiplication and division inequalities?. Solving Inequalities by Multiplication & Division.

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Solving Inequalities by Multiplication & Division

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  1. Solving Inequalities by Multiplication & Division

  2. Solving Inequalities by Multiplication & Division Objective: • 7.5.03 Essential Question: • How can we use inverse operations to solve one step multiplication and division inequalities?

  3. Solving Inequalities by Multiplication & Division Review: • < • - is less • than • - is fewer than • > • - is more than • - is greater than • ≤ • - is less than or equal to • - is no more than • ≥ • - is greater than or equal to • - is no less than

  4. Solving Inequalities by Multiplication & Division Real World: As a salesperson, Kim is paid $75 per week plus $5 per sale. This week you want to pay her at least $120. Write an inequality and find how many sales Kim will need to complete to make $120. Inequality: 5s + 75 ≥ 120 Kim needs to make at least 9 sales.

  5. Solving Inequalities by Multiplication & Division Example 1:Solve 2z > 20. 2z > 20 2 2 • z > 10

  6. Solving Inequalities by Multiplication & Division Example 1:Solve 2z > 20. 2z > 20 2 2 • z > 10 • 7 8 9 10 11 12 13

  7. Solving Inequalities by Multiplication & Division • Example 2:Solve ½p ≤ 8. • (2)½p ≤(2)8

  8. Solving Inequalities by Multiplication & Division • Example 2:Solve ½p ≤ 8. • (2)½p ≤(2)8 • p ≤ 16

  9. Solving Inequalities by Multiplication & Division • Example 2:Solve ½p ≤ 8. • (2)½p ≤(2)8 • p ≤ 16 • 13 14 15 16 17 18 19

  10. Solving Inequalities by Multiplication & Division The Tricky Trick: • BUT WHAT HAPPENS WHEN WE MULTIPLY OR DIVIDE AN INEQUALITY BY A NEGATIVE NUMBER…

  11. Solving Inequalities by Multiplication & Division The Tricky Trick: • - When we multiply or divide each side of an inequality by a negative number, we must reverse the sign of the inequality for it to remain true… • Example: 4 < 9 • (-1)(4) > (-1)(9) • - 4 > - 9

  12. Solving Inequalities by Multiplication & Division Example 3:Solve – 8r > 48. – 8r > 48i

  13. Solving Inequalities by Multiplication & Division Example 3:Solve – 8r > 48. • – 8r> 48i • – 8– 8 • r < – 6

  14. Solving Inequalities by Multiplication & Division Example 3:Solve – 8r > 48. • – 8r> 48i • – 8 – 8 • r < – 6 • -9 -8 -7 -6 -5 -4 -3

  15. Solving Inequalities by Multiplication & Division Example 4:Solve m/(– 3) ≤ 5. • (-3) • m ≤ 5i• (-3) • – 3

  16. Solving Inequalities by Multiplication & Division Example 4:Solve m/(– 3) ≤ 5. • (-3) • m ≤ 5i• (-3) • – 3

  17. Solving Inequalities by Multiplication & Division Example 4:Solve m/(– 3) ≤ 5. • (-3) • m ≤ 5i• (-3) • – 3 • m ≥ – 15

  18. Solving Inequalities by Multiplication & Division Example 4:Solve m/(– 3) ≤ 5. • (-3) • m ≤ 5i• (-3) • – 3 • m ≥ – 15 • -18 -17 -16 -15 -14 -13 -12

  19. Solving Inequalities by Multiplication & Division Flip Rule: WHEN YOU (X) or (÷) BY A NEGATIVE YOU ALWAYS FLIP THE INEQUALITYSIGN

  20. Solving Inequalities by Multiplication & Division Independent Practice: • Solve and graph each inequality below. • 1. 4w ≥ 48 • 2. 6 < s/5 • 3. – m > – 27 • 4. – 9p ≤ – 72 • 5. – 15 < g/3

  21. Solving Inequalities by Multiplication & Division Independent Practice: • Answers. • 1. 4w ≥ 48 1. w ≥ 12 • 2. 6 < s/5 2. s < 30 • 3. – m > – 27 3. m < 27 • 4. – 9p ≤ – 72 4. p ≥ 8 • 5. – 15 < g/35. g <– 45

  22. Solving Inequalities by Multiplication & Division HOMEWORK

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