Question

find the linear equation
9x-(3+4x)/2x-(7-5x)=6/7​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf \longmapsto \dfrac{9x - (3 + 4x)}{2x - (7 - 5x)} = \dfrac{6}{7}$

$\sf \longmapsto \dfrac{9x - 3 - 4x}{2x - 7 + 5x} = \dfrac{6}{7}$

$\sf \longmapsto \dfrac{9x - 4x - 3}{2x + 5x - 7} = \dfrac{6}{7}$

$\sf \longmapsto \dfrac{5x - 3}{7x - 7} = \dfrac{6}{7}$

Cross multiply to both sides :

$\sf \longmapsto7(5x - 3) = 6(7x - 7)$

$\sf \longmapsto35x - 21 = 42x - 42$

Taking 7 both sides as all are multiple of 7.

$\sf \longmapsto7(5x - 3) = 7(6x - 6)$

7 on both sides so,it gets automatically cancelled

$\sf \longmapsto5x - 3 = 6x - 6$

$\sf \longmapsto5x - 6x = - 6 + 3$

$\sf \longmapsto - x = - 3$

$\sf \large\bold{\red{x = 3}}$

Check:

$\sf \longmapsto \dfrac{9x - 3 - 4x}{2x - 7 + 5x}$

$\sf \longmapsto \dfrac{9 \times 3 - 3 - 4 \times 3}{2 \times 3 - 7 + 5 \times 3}$

$\sf \longmapsto \dfrac{27 - 3 - 12}{6 - 7 + 15}$

$\sf \longmapsto \dfrac{27 - 15}{6 + 8} = \dfrac{12}{14} = \dfrac{6}{7}$