Solve each of the following in equations and represent the solution set on the number line.

, where x ϵ R.

Given:

, where x ϵ R.

Multiply by 12 on both sides in the above equation

(2x - 1) – 4(x - 1) < 3(3x + 1)

2x – 1 – 4x + 4 < 9x + 3

3 – 2x < 9x + 3

Now, subtracting 3 on both sides in the above equation

3 – 2x – 3 < 9x + 3 - 3

-2x < 9x

Now, subtracting 9x from both the sides in the above equation

-2x – 9x < 9x – 9x

- 11x < 0

Multiplying -1 on both the sides in above equation

(-11x)(-1) < (0)(-1)

11x > 0

Dividing both sides by 11 in above equation

Therefore,

x > 0