How do you solve the absolute value abs(3x-1) + 10 = 25?

1 Answer
MeneerNask
May 13, 2015

Actually there are two conditions to look at:

(1) If 3x-1>=0 we have:

(3x-1)+10=25->3x=25+1-10=16->
x=16//3=5 1/3

(2) If 3x-1<0 the absolutes 'turn it around':

-(3x-1)+10=25->-3x=25-1-10=14->
x=14//(-3)=-4 2/3

Validation:
(allways do this, sometimes one of the answers is wrong)
(1) exists if x>=1/3 which is consistent with the answer
(2) exists if x<1/3 which is also consistent with the answer

Final answer: x=5 1/3orx=-4 2/3

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