# How do you solve #1<abs(s-2)<3#?

##### 2 Answers

It's complicated.

#### Explanation:

First let's split this into two parts.

Here's where things get confusing. Absolute value means that the number could either be positive or negative. If it's negative, the sign is flipped.

Wait, look at that 2nd part. If s can be less than 5 (a bigger number), or more than -1 (a smaller number), then s can be anything (at least in one conditional). So this can be rephrased as:

The "and" means that 's' can be anything where these 2 conditionals overlap. It's pointless to ask if something overlaps with all real numbers, so we can get rid of that, leaving us with the final answer:

There is no one sentence "How".

The solution set is:

#### Explanation:

**Algebraic solution**

**Geometric solution**

So

On the number line, find

Look on the right for the points (numbers) more than

Look on the left for the points (numbers) more than

So we need s to be between