How do you solve #absx - 4 =3x#?

1 Answer
MeneerNask
Jul 6, 2015

There are two possible solutions, depending on whether #x# is positive or not.

Explanation:

#x>=0#
Then the equation turns into:
#x-4=3x->-4=2x->x=-2#
This in contrary to the #x>=0# condition, so this solution has to be discarded.

#x<0#
The sign for x is reversed, and the equation becomes:
#-x-4=3x->-4=4x->x=-1#
And this is acceptable.
Check: #|-1|-4=3*(-1)->1-4=-3#

Conclusion:
The only solution: #x=-1#

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