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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.

\(\frac{{\text{x}}}{4} < \frac{(5{\text{x}}-2)}{3} - \frac{(7{\text{x}}-3)}{5}\), where x ϵ R.

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1 Answer

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by (15.2k points)

Given:

\(\frac{{\text{x}}}{4} < \frac{(5{\text{x}}-2)}{3} - \frac{(7{\text{x}}-3)}{5}\), where x ϵ R.

Multiplying 60 on both the sides in the above equation,

\(\frac{{\text{x}}}{4}(60) < \frac{(5{\text{x}}-2)}{3}(60) - \frac{(7{\text{x}}-3)}{5}(60)\)

15x < 20(5x - 2) – 12(7x - 3) 

15x < 100x – 40 – 84x + 36 

15x < 16x – 4 

Now, subtracting 16x from both sides in above equation 

15x – 16x < 16x – 4 – 16x

-x < -4 

Now, multiplying by -1 on both sides in above equation 

(-x)(-1) < (-4)(-1) 

x > 4 (inequality sign reversed)

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