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in Linear Equations by (15.7k points)

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

\(\frac{2{\text{x}} - 1}{12} - \frac{{\text{x}}-1}{3}<\frac{3{\text{x}}+1}{4} \) , where x ϵ R.

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by (15.2k points)

\(\frac{2{\text{x}} - 1}{12} - \frac{{\text{x}}-1}{3}<\frac{3{\text{x}}+1}{4} \) , 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

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