# Solving Radical Inequalities

How to solve radical inequalities: examples and their solutions.

## Example 1

First, find the range of *x*.

2*x* - 3 is the radicand of the square root.

So 2*x* - 3 ≥ 0.*x* ≥ 3/2

To remove the radical sign,

square both sides.

The order of the inequality sign doesn't change

because both sides (√2*x* - 3, 5) are (+).

Then *x* < 14.

Draw *x* ≥ 3/2 and *x* < 14 on a number line.

Graphing linear inequalites on a number line

Find the intersecting region:

3/2 ≤ *x* < 14.

## Example 2

Find the ranges of *x*.*x* is the radicands of the square root.

So *x* ≥ 0.*x* - 2 is also the radicands of the square root.

So *x* - 2 ≥ 0.*x* ≥ 2

To remove the radical sign of √*x*,

square both sides.

To remove the radical sign of √*x* - 2,

leave only √*x* - 2 on the left side,

and square both sides again.

Draw *x* ≥ 0, *x* ≥ 2, and *x* < 9/4 on a number line.

Graphing linear inequalites on a number line

Find the intersecting region:

2 ≤ *x* < 9/4.