Home > Algebra > Absolute Value Inequalities

How do you solve #abs( x + 3) <2#?

Answer 1

Hazel Anglin

#x< -1 and x> -5#
In interval notation solution is #(-5, -1)#

#|x+3| < 2 ; x+3 < 2 and x+3 > -2 :. x< -1 and x> -5# In interval notation solution is # (-5, -1)#[Ans]

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Abigail Allen

To solve the inequality |x + 3| < 2, you first isolate the absolute value expression by considering two cases: when the expression inside the absolute value is positive and when it's negative.

Case 1: x + 3 ≥ 0 x + 3 < 2 x < -1

Case 2: x + 3 < 0 -(x + 3) < 2 -x - 3 < 2 -x < 5 x > -5

Combining both cases: -5 < x < -1

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #abs( x + 3) &lt;2#?

How do you solve #abs( x + 3) <2#?