How do you solve abs(2t-3) = t and find any extraneous solutions?

1 Answer
Dean R.
May 4, 2018

t=1 or t=3 and despite squaring equations, no extraneous solutions suggested themselves.

Explanation:

Squaring usually introduces extraneous solutions. It's worth it because it turns the whole thing to straightforward algebra, eliminating the confusing case analysis typically associated with an absolute value question.

(2t-3)^2 = t^2

4t^2 - 12 t + 9 = t^2

3(t^2 -4t + 3) = 0

(t-3)(t-1)=0

t=3 or t=1

We're in good shape because no negative t values came up, which are surely extraneous, We'll check these two but they should be OK.

|2(3) - 3| = |3|=3=t quad sqrt

|2(1)-3| = |-1|=1=t quad sqrt

Related questions
See all questions in Absolute Value Equations
Impact of this question
1473 views around the world
You can reuse this answer
Creative Commons License