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