Solve the inequality |4x-3|<|2x+1|.

There are two ways to solve this problem. The easiest way is graphically, but that requires little explanation and I am not sure how to show graphs on here so I will explain it algebraically.Because both sides of the inequality sign have a modulus sign around them they somewhat will cancel out so that there are only two possible cases. The first is that (4x-3)<(2x+1). We can rearrange this to get 2x<4 and then divide both sides by 2 to get x<2. The other possible case is that (4x-3)>-(2x+1). In this case we can simplify to (4x-3)>(-2x-1). Then rearrange to get 6x>2. We then divide both sides by 6 to get x>(1/3). We can combine these answers to get (1/3)<x<2. I would then advise you to check the solution graphically.