3-3 Solving Inequalities Using Multiplication and Division

3-3 Solving Inequalities Using Multiplication and Division

10 < 15

multiply both sides by 2

is it true?

10 < 15

divide both sides by 5

is it true?

10 < 15

multiply both sides by -2.

is it true?

NO! -20 is not less than -30!

10 < 15

Divide both sides by -5 is it true?

NO! -2 is not less than -3

Multiplication/Division Property of Inequality

When you multiply or divide both sides of an inequality by the same positive number it remains true.

When you multiply or divide both sides of an inequality by the same negative number then you must flip the sign to keep it true!

Multiple Choice

 $\frac{c}{8}>\frac{1}{4}$  What is the solution for Problem 1 Got it?

•  $c>4$  

•  $c>2$  

•  $c<2$  

•  $c>\frac{1}{2}$  

Multiple Choice

What is the graph for your solution to Problem 1 Got it?

Problem 2 Got it?

 $-\frac{n}{3}<-1$  


solve and graph

Multiple Choice

What was your solution for problem 2 got it?

 $-\frac{n}{3}<\ -1$  

•  $n<3$  

•  $n<-3$  

•  $n>3$  

•  $n>-3$  

Multiple Choice

What is the graph for Problem 2 Got it?

Multiple Choice

Which inequality represents this?

• $10.68c\ge50$

• $\frac{c}{10.68}\ge50$

• $10.68c\le50$

Multiple Choice

 Would you have to flip the sign when you solve the inequality from this problem 
 $10.68c\le50$  

• yes

• no

Multiple Choice

What is the solution to the word problem?

• 4 cases or less

• 5 cases or left

Multiple Choice

 $-5x>-10$  

What are the solutions to problem 4 got it?

•  $x<2$  

•  $x\le2$  

•  $x>2$  

•  $x>-2$  

Multiple Choice

13a > -26

• a > -2

• a < -2

• a > 1/2

• a < -1/2

Multiple Choice

-8x < 48

• x < -6
• x > -6
• x < 6
• x > 6

Multiple Choice

Solve
-5m < 10

• m < -2
• m > -2
• m < -50
• m > -50

Multiple Choice

8x < 48

• x < -6
• x > -6
• x < 6
• x > 6