# How do you solve #abs(2x)<2+ abs3#?

##### 1 Answer

First of all, simplify the inequality.

Since

Both sides of an inequality can be divided by a positive constant without changing the sign of inequality, and the new inequality will be equivalent to an old one.

Let's divide out equation by

The solution to this inequality is, obviously,

The above solution can be obtained using the following logic:

By definition,

Therefore, we can look for solutions of our inequality for

**Case 1**. Assume

Then

Combining this with a requirement

**Case 2**. Assume

Then

Combining this with a requirement

Combining two areas that represent solutions,

we obtain one interval for