Question

Solve the inequalities in exercieses 17 to 20 and show the graph of the solution in each case on number line.

$\frac{x}{2}\ge \frac{(5x-2)}{3}-\frac{(7x-3)}{5}$

Answer 1

Here $\frac{x}{2}\ge \frac{(5x-2)}{3}-\frac{(7x-3)}{5}$

$\Rightarrow \frac{x}{2}\ge \frac{5x}{3}-\frac{2}{3}-\frac{7x}{5}+\frac{3}{5}$

$\Rightarrow \frac{x}{2}-\frac{5x}{3}+\frac{7x}{5}\ge \frac{-2}{3}+\frac{3}{5}$

$\Rightarrow \frac{15x-50x+42x}{30}\ge \frac{-10+9}{15}\Rightarrow \frac{7x}{30}\ge \frac{-1}{15}$

Multiplying both sides by 30, we have

$7x\ge -2$

Dividing both sides by 7, we have

$x\ge \frac{-2}{7}$

The solution set is $[\frac{-2}{7},\infty ).$

The representation of the solution set on the number line is