Solving Inequalities by Multiplication & Division.

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Presentation transcript:

Solving Inequalities by Multiplication & Division

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Independent Practice: Answers. 1. 4w ≥ 481. w ≥ < s/52. s < – m > – 273. m < – 9p ≤ – 724. p ≥ 8 5. – 15 < g/35. g < – 45 Solving Inequalities by Multiplication & Division

HOMEWORK Solving Inequalities by Multiplication & Division