SOLUTION: Write the absolute value inequality in the form |x−b|<c or |x−b|>c that has the solution set x<−5 or x>7.

Mark -5 and 7 on a number line with open circles since the inequalities
are < and > and not < or > and graph the solution set.


<=========o-----------------------------------o========>
-8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10

Find the midpoint between -5 and 7 by averaging them:



Count how many units 1 is from -5 and from 7. (They should be the same
if you got their average correctly)

I get (by counting units) that 1 is 6 units from both -5 and 7.

So we need to say this in symbols: 

"for a number x on the number line to be in the shaded part, the difference
between it and the midpoint 1 (in absolute value) must be greater than 6 
units."

To say that in symbols, we express the difference between x and 1 by 
indicating a subtraction of x and 1 with "x-1", and putting absolute
values around it, like this |x-1| and indicating that it must be
greater than 6 units away from the midpoint 1:

|x-1| > 6

Edwin