How do you solve # 3x+5=abs(x-6)#?

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Answer 1 · 2018-03-14T09:00:12

#x=0.25#

Because of the absolute value function (#abs()#), the function inside can be positive or negative.

#3x+5=x-6# or #3x+5=6-x#

#2x=-11# or #4x=1#

#x=-11/2 or 1/4#

Now to check:
#3(0.25)+5=23/4#
#abs(0.25-6)=23/4#

#3(-11/2)+5=-23/2#
#abs(-11/2-6)=23/2#

So, #x=0.25#