|x-7| < -4

Solution: Since this is a "less than" absolute value inequality, the first step is to clear the absolute value according to the pattern

|x-7| < -4

-4<x-7<4

-4+7 < x-7+7 < 4+7

3 < x <11

Then the solution to |x-7| < -4 is the interval 3 < x <11