# How do you solve #abs(x-10)>=20#?

##### 2 Answers

Use the piecewise definition:

Solve the two inequalities.

Check.

#### Explanation:

Given:

Use the piecewise definition:

Multiply both sides of the second inequality by -1:

Add 10 to both sides of both inequalities:

Check the equality points:

Check 31 and -11:

This checks.

Absolute value inequality. Okay. Here we go.

#### Explanation:

We have:

The absolute value of

So either:

(Just like

First let's solve

Add

We get

Next let's solve

Multiply the

Subtract

At this point, we need to multiply both sides of the inequality by

When you **multiply or divide an inequality by a negative number** , you have to **change the direction of the inequality** , so we get:

The solution to this inequality is in two parts:

**OR**

You can write this in interval notation as:

Parentheses: that endpoint **is not** included in the interval - when you have only

Square brackets: that endpoint **is** included in the interval - when you have

**Union** of two sets - the two parts - written

Here's a line graph of the solution:

****************]---------------|------------------------[******************>

The dots between the

The asterisks are shaded parts of the line to indicate that this part of the Real Number Line is part of the solution to the inequality.

I'll come back and edit this answer if I can get a better graph going.

Connie