Question

The graph of solution of the inequality $\frac{x}{2}\ge \frac{5x-2}{3}-\frac{7x-3}{5}$ on the number line is

• A.
• B.
• C.
• D. None of the above

Answer 1

Answer: (A)

We have, $\frac{x}{2}\ge \frac{(5x-2)}{3}-\frac{(7x-3)}{5}$
Taking LCM in RHS,
$\frac{x}{2}\ge \frac{5(5x-2)-3(7x-3)}{15}$
$\Rightarrow \frac{x}{2}\ge \frac{25x-10-21x+9}{15}$
$\Rightarrow \frac{x}{2}\ge \frac{(25x-21x)-(10-9)}{15}$
$\Rightarrow \frac{x}{2}\ge \frac{4x-1}{15}$
$\Rightarrow 15x\ge 2(4x-1)$
$\Rightarrow 15x\ge 8x-2$
Transferring the term $8x$ to LHS,
$15x-8x\ge -2\Rightarrow 7x\ge -2$
Dividing both sides by 7 ,
$\frac{7x}{7}\ge \frac{-2}{7}\Rightarrow x\ge -\frac{2}{7}$