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 Review: - is less than - is more than - is fewer than - is greater than - is less than or equal to - is greater than or equal to - is no more than - 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 20 2 2 z 10

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

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 16 13 14 15 16 17 18 19

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 –6 -9 -8 -7 -6 -5 -4 -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

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 – 15 -18 -17 -16 -15 -14 -13 -12

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 48 2. 6 s/5 3. – m – 27 4. – 9p – 72 5. – 15 g/3

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/3 5. g – 45

Solving Inequalities by Multiplication & Division HOMEWORK