How do you solve abs(4-3x)= 4x + 6 and state the extraneous solutions?

1 Answer
Apr 22, 2015

abs(4-3x) = 4x+6

Consider the two possibilities for (4-3x)

Possibility 1:
(4-3x)<0
rarr x>4/3

abs(4-3x) = 4x +6
becomes
3x-4 = 4x+6
x=-10
but x>4/3 for this condition to apply
so this solution is extraneous.

Possibility 2:
(4-3x)>=0
rarr x<= 4/3

abs(4-3x)= 4x+6
becomes
4-3x = 4x+6
x = 2/7

Since x=2/7 satisfies the condition x<= 4/3
this is a valid solution