Question

Solve the inequalities and show the graph of the solution on number line: $\frac{x}{2} \geq \frac{(5x-2)}{3}- \frac{(7x-3)}{5}$

Answer 1

$\dfrac{x}{2} \geq \dfrac{(5x-2)}{3}- \dfrac{(7x-3)}{5}$

$\dfrac{x}{2} \geq \dfrac{5(5x-2)}{15}- \dfrac{3(7x-3)}{15}$

$\dfrac{x}{2} \geq \dfrac{25x-10}{15}- \dfrac{21x-9}{15}$

$\dfrac{x}{2} \geq \dfrac{25x-10 - 21x + 9}{15}$

$\dfrac{x}{2} \geq \dfrac{4x-1}{15}$

$15x \geq 2(4x - 1)$

$15x \geq 8x - 2$

$7x \geq - 2$

$x \geq -\dfrac{2}{7}$