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

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Answer 1 · 2018-03-03T01:08:32

The solutions are #x=0,10#.

There are two possible solutions to an absolute value equation.

For example, the solutions for #|x|=1# are #x=1# and #x=-1#, because the absolute values of #1# and #-1# are both #1#.

The equation #|x-5|=5# splits into to solutions: #x-5=5# and #x-5=-5#. Now, solve for #x# in both of the new equations.

#qquadqquadqquadqquad|x-5|=5#
#" ↙ ↘"#
#color(white){color(black)( (x-5=5, qquadqquad x-5=-5), (x=10, qquadqquad x=0)):}#

Those are the two solutions. We can verify them by plugging them into the original equation:

#|x-5|=5#

Check #0#:

#|0-5|=5#

#|-5|=5#

#5=5" "sqrt#

The solution #0# works. Check #10#:

#|10-5|=5#

#|5|=5#

#5=5" "sqrt#

The solution #10# also works, so both solutions are correct. Hope this helps.

Answer 2 · 2018-03-03T01:19:35

#x=0 or 10#

#x-5 =5# or #x-5=-5#
#x=5+5# or #x=-5+5#
#x=10# or #x=0#