Solve |x| + 7 < 4.
This inequality has no solution:
l X l + 7 < 4
l x l ≥ 0 , is always positive , therefore, l x l + 7 , could never be < 7.
Solve |x| + 7 < 4.
There is no set of numbers that will work here, because x is represented in terms of absolute value. If the question asked simply what set of values for x would fit, the answer would be x<-11.