How do you solve one-variable inequalities?

For example, how do you know what values of x make the following inequality true?

-4(x – 5) > 2x + 10

In this lesson you will learn how to solve inequalities by

using additive and multiplicative inverses.

Let’s Review

Addition Property of Inequality

4 < 5 2 + + 26 < 7

4 < 5 (-2) + + (-2)

2 < 3

Let’s Review

Multiplication Property of Inequality4 < 52 x x 28 < 10

4 < 5(-2) x x (-2)

-8 <-10-8 > -10

A Common Mistake

Forgetting that the multiplication property of inequality may mean that you need to switch the direction of the

inequality sign.

-4x > 16 x - 1

4 14

x -

x < -4

Core Lesson x #3x > 2x + 7-2x -2x

x > 7

Check:x = 9

3(9) > 2(9) + 7

9 > 7

Core Lesson -4(x – 5) < 2x + 8 -4x + 20 < 2x + 8

x #

-20 -20

-4x < 2x - 12-2x -2x

-6x < -12

x > 2

Check:

-4(5 – 5) < 2(5) + 10

x = 5

5 > 2

x - 16

16

x -

In this lesson you have learned how to solve inequalities by

using additive and multiplicative inverses.

Guided Practice

4x – 15 > -3(8 – 4x)

Extension Activities

Describe one extension activity here…

Please add extension activity

Extension Activities

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Quick Quiz

5x + 23 < 3 – 4x + 2

4x – 7x + 2 > 4 + 5x