Thread: please check my work...

|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

Originally Posted by bobby77

|x-7| < -4

This has no real solutions. The Left Hand Side of the inequality is always
greater than or equal to zero, while the Right Hand Side is less than zero.

So you are being asked to find an x to make a non-negative number less
than a negative number which can't be done.

RonL