How do you solve # |x-7|=4#?

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Answer 1 · 2017-09-13T18:29:51

The piecewise definition of the absolute value function is:

#|f(x)| = {(f(x); f(x)>=0),(-f(x); f(x)< 0):}#

This allows us to separate #|x-7| = 4# into two equations:

#x - 7 = 4# and #-(x-7) = 4#

Multiply the second equation by -1:

#x - 7 = 4# and #x-7 = -4#

Add 7 to both sides of both equations:

#x = 11# and #x = 3#

Check:

#|11-7| = 4# and #|3-7|=4#

#|4| = 4# and #|-4|=4#

Both check.