# What are Equivalent Inequalities? Definition and Examples

What are equivalent inequalities? Equivalent inequalities are inequalities that have the same solutions. For example, x + 3 > 8 and x > 5 are equivalent inequalities.

Why are x + 3 > 8 and x > 5 equivalent inequalities? Just subtract 3 from each side of x + 3 > 8 and you will end up with x > 5.

x + 3 > 8

x + 3 - 3 > 8 - 3

x > 5

## More examples of equivalent inequalities

**1.**

4x > 36 and x > 9 are equivalent inequalities. Just divide each side of 4x > 36 by 4 and you will end up with x > 9.

**2.**

5x + 2 > 17 and x > 3 are equivalent inequalities. First subtract 2 from each side of 5x + 2 > 17 and then divide each side by 5.

5x + 2 > 17

5x + 2 - 2 > 17 - 2

5x > 15

5x / 5 > 15 / 5

x > 3

**3.**

x > 8 and 8 < x are equivalent inequalities. If x is bigger than 8, then 8 is smaller than x.

**4.**

-2x < 8 and x > -4 are equivalent inequalities. Divide each side of -2x < 8 by -2 and change < to >. Read this lesson to understand why we replaced < with >

-2x < 8

-2x / -2 > 8 / -2

x > -4

## Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

- Click on the HTML link code below.
- Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.