Solve the inequality and represent them on a number line (i) 4x+1/3>2x/3-2 (ii) 1x/3-2<2x/5+1/4?

(i) 4x + 1/3 > 2x/3 - 2

First, let's get rid of the fractions by multiplying everything by 3:

12x + 1 > 2x - 6

Next, let's isolate x by subtracting 2x from both sides and subtracting 1 from both sides:

10x + 1 > -6
10x > -7
x > -7/10

So the solution to the inequality is x > -7/10.

(ii) 1x/3 - 2 < 2x/5 + 1/4

First, let's get rid of the fractions by multiplying everything by 60 (the least common multiple of 3, 5, and 4):

20x - 120 < 24x + 15

Next, let's isolate x by subtracting 20x from both sides and adding 120 to both sides:

-4x < 135
x > -135/4

So the solution to the inequality is x > -135/4.