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How do you solve one-variable inequalities?

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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.

Addition Property of Inequality

2 + + 2

4 < 5

6 < 7

(-2) + + (-2)

4 < 5

2 < 3

Multiplication Property of Inequality

2 xx 2

4 < 5

8 < 10

(-2) xx (-2)

4 < 5

-8 <-10

-8 > -10

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

x-

1

1

-4x > 16

4

4

x-

x < -4

x #

3x > 2x + 7

-2x -2x

Check:

x = 9

x > 7

9 > 7

3(9) > 2(9) + 7

x #

-4(x – 5) < 2x + 8

Check:

-4x + 20 < 2x + 8

x-

-20 -20

x = 5

-4x < 2x - 12

5 > 2

1

1

-2x -2x

6

6

-4(5 – 5) < 2(5) + 10

-6x < -12

x-

x > 2

In this lesson you have learned how to solve inequalities by using additive and multiplicative inverses.

4x – 15 > -3(8 – 4x)

Please add extension activity

- Describe one extension activity here…

- Describe another extension activity here…

5x + 23 < 3 – 4x + 2

4x – 7x + 2 > 4 + 5x