How do you solve abs(4x-3)<7?

1 Answer
Jul 28, 2016

-1 < x < 2.5 - i.e. x is between -1 and 2.5

Explanation:

As |4x-3|<7,

either 4x-3<7 i.e, 4x<7+3 or

4x=10 i.e. x<10/4 i.e. x<2.5

or -(4x-3)<7 i.e. -4x+3<7 or

3-7<4x or 4x>-4 i.e. x>-1

Hence, we have x<2.5 and x>-1, which can be written better as

-1 < x < 2.5 - i.e. x is between -1 and 2.5