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.

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