# What do you do when you have absolute values on both sides of the equations?

##### 2 Answers

Please read the explanation.

#### Explanation:

When we have **absolute values** on both sides of the equations,

we must consider both possibilities for acceptable solutions - **positive and negative** absolute value expressions.

We will look at an example first to understand:

**Example-1**

Solve for

Both sides of the equation contain **absolute values**.

Find solutions as shown below:

**.. Exp.1**

**...Exp.2**

Consider **... Exp.1** first and solve for

Add

Add

Divide both sides by

**... Sol.1**

Consider **... Exp.2** next and solve for

Subtract

Add

Divide both sides of the equation by

**... Sol.2**

Hence, there are **two solutions** for the absolute value equation:

**... Sol.1**

**... Sol.2**

If you so wish, you can **substitute** these values of

We will work on **Example.2** in my next answer.

Hope it helps.

**Example.2** is given here.

#### Explanation:

This is a continuation of my solution given earlier.

We worked on **Example.1** in that solution.

Please refer to that solution first, before reading this solution.

Let us consider a second example:

**Example.2**

Solve for

Subtract

Divide both sides by

Subtract

Hence, we conclude that

Hope it helps.