4.3k views
3 votes
What is the solution set for 1<_|x+3|<_4

1 Answer

4 votes

The solution set for 1<|x+3|<4 is:

x ∈ (-2, 2)

To solve this inequality, we first need to isolate the absolute value. This gives us:

|x+3| - 1 < 4 - 1

We can then remove the absolute value signs by considering two cases:

* Case 1: x + 3 > 0

In this case, we have:

x + 3 < 5

Solving for x, we get:

x < 2

* Case 2: x + 3 < 0

In this case, we have:

-(x + 3) < 5

Multiplying both sides by -1, we get:

x + 3 > -5

Solving for x, we get:

x > -8

Combining the solutions from both cases, we get:

x ∈ (-2, 2)

User Pzulw
by
7.8k points

Related questions

asked Jun 18, 2024 201k views
Panoet asked Jun 18, 2024
by Panoet
8.4k points
2 answers
5 votes
201k views
1 answer
2 votes
217k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.