The set of all real number x such

fernandoval3sbr

fernandoval3sbr

Answered question

2022-04-10

The set of all real number x such that
||3x||x+2=5

Answer & Explanation

gsmckibbenx7ga

gsmckibbenx7ga

Beginner2022-04-11Added 17 answers

There is no need for squaring. Squaring has a risk of introducing extraneous solutions. Instead we can say
|3-x|-|x+2|=±5   (1)
Now consider three cases:
x3. In this case equation (1) becomes
3+xx2=±55=5  OR  5=5
Because of the latter, x3 is a solution interval.
Now do the same for 2x<3 and x<2.

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