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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