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Solve the inequality and show the graph of the solution on number line x / 2 greater than or equal to (5x - 2) / 3 - (7x - 3) / 3

Solve the inequality and show the graph of the solution on number line

    Q20.    \frac{x}{2} \geq \frac{(5x-2)}{3} - \frac{(7x-3)}{5}

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Given :   \frac{x}{2} \geq \frac{(5x-2)}{3} - \frac{(7x-3)}{5}

\Rightarrow      \frac{x}{2} \geq \frac{(5x-2)}{3} - \frac{(7x-3)}{5}

\Rightarrow \, \, \, 15x \geq 10(5x-2) - 6(7x-3)

\Rightarrow \, \, \, 15x \geq 50x-20 - 42x+18

\Rightarrow \, \, \, 15x+42x-50x \geq 18-20

\Rightarrow \, \, \, 7x \geq -2

\Rightarrow \, \, \, x \geq \frac{-2}{7}

 x are  real numbers greater than  equal to = \frac{-2}{7}

Hence, values of x can be  as  x\in (-\frac{2}{7},\infty )

The graphical representation of solutions of the given inequality is as : 

 

 

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