\(\frac{2{\text{x}} - 1}{12} - \frac{{\text{x}}-1}{3}<\frac{3{\text{x}}+1}{4} \) , where x ϵ R
Multiply by 12 on both sides in the above equation
\(12\big(\frac{2{\text{x}} - 1}{12}\big) -12\big(\frac{{\text{x}}-1}{3}\big)<12\big(\frac{3{\text{x}}+1}{4}\big)\)
(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
\(\frac{11x}{11}>\frac{0}{11}\)
Therefore,
x > 0