# How do you solve #x^4<4x^2#?

##### 1 Answer

i.e.

#### Explanation:

First note that if

If

#x^2 < 4#

**Case #bb(x > 0)#**

Since

#x < 2#

Hence we have solutions:

#0 < x < 2#

**Case #bb(x < 0)#**

Note that

#-x < 2#

Multiplying both sides by

#x > -2#

Hence we have solutions:

#-2 < x < 0#

**Background**

The truth or falsity of an inequality is unaltered by any of the following operations:

- Add or subtract the same value from both sides.
- Multiply or divide both sides by the same positive value.
- Multiply or divide both sides by the same negative value and
**reverse the inequality**(#<# becomes#># ,#>=# becomes#<=# , etc.).

More generally:

- Apply the same strictly monotonically increasing function to both sides of the inequality.
- Apply the same strictly monotonically decreasing function to both sides of the inequality and
**reverse the inequality**.