Section 6.2: Solving Inequalities Using Multiplication and Division

Section 6.2: Solving Section 6.2: Solving Inequalities Using Inequalities Using Multiplication and DivisionMultiplication and Division

Activity 4 ____ 3Activity 4 ____ 3Complete the table with <, >

or =

What happens to the inequality symbol when you multiply each side by a positive number

What happens to an inequality symbol when you multiply each side by 0

What happens to an inequality symbol when you multiply each side by a negative number

4 * 3 1 * 3

4 * 2 1 * 2

4 * 1 1 * 1

4 * 0 1 * 0

4 * -1 1 * -1

4 * -2 1 * -2

4 * -3 1 * -3

Now try solving these Now try solving these inequalitiesinequalities -3x > 15

-4x < 12

After you and your table partner solve, pick a number to see if it is a solution.

How is this like the first activity you and your table partner did.

Solving inequalities: Use Solving inequalities: Use Multiplication and DivisionMultiplication and Division*Remember – Solve the inequality

by getting the variable by itself. Use inverse operations!!!*

- Inverse operation of multiplication is division

- Inverse operation of division is multiplication

Second reminder!!!Second reminder!!!

When graphing inequalities…< , > means open circle

< ,> means closed circle

Important Note!!!Important Note!!!

*Note – You must reverse the direction of the inequality sign when you multiply or divide each side by a negative number.

Examples when you should reverse the inequality sign:

(1) -2x > 8 (2) 2

3

x

Examples:Examples:

Directions: Solve each inequality and graph the solution on a number line.

(1) 8x > 16 (2) -4x < 12

(3) (4) 27

x 4

3

2x

Try these:Try these:

Directions: Solve each inequality and graph the solution on a number line.

(1) 3x > 9 (2) -5x < 20

(3) (4) 23

x

34

3x