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

Answer 1

Eva Adamson

Interpreting the modulus, this means

#-2 < 2x - 3 < 2#

Add #3# to all parts to get:

#1 < 2x < 5#

Divide all parts by #2# to get:

#1/2 < x < 5/2#

In general you can do the following to an inequality and maintain its truth (or falsity):

(1) Add or subtract the same value on both sides. (2) Multiply or divide both sides by the same positive value. (3) Multiply or divide both sides by the same negative value and reverse the inequality (#<# becomes #>#, #>=# becomes #<=#, etc.).

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

Answer 2

Ethan Adkins

To solve the inequality |2x - 3| < 2, you would first isolate the absolute value expression, then consider two cases: when the expression inside the absolute value is positive and when it's negative. Finally, you would solve each case separately to find the solution set for the inequality.

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(2x-3)&lt;2#?

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