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