Question

solve
2x - 7 / x + 4 = 3 / 4​

Answer 1

$\: \: \: \: \: \: \: \: \: \: \: \: \frac{2x - 7}{x + 4} = \frac{3}{4} \\ = = > 4(2x - 7) = 3(x + 4) \\ = = > 8x - 28 = 3x + 12 \\ = = > 8x - 3x = 12 + 28 \\ = = > \: \: \: \: \: \: 5x = 40 \\ = = > \: \: \: \: \: \: x = \frac{40}{5} = 8$

Answer 2

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

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

Now,cross multiply to both sides:

$\sf \longmapsto4(2x - 7) = 3(x + 4)$

$\sf \longmapsto8x - 28 = 3x + 12$

Now, arranging the terms making like terms together:

when 3x shifts towards left hand side it's sign gets changed from +ve to -ve.Similarly, -28 will be +28 when it shifts towards right hand side.

$\sf \longmapsto8x - 3x = 12 + 28$

$\sf \longmapsto5x = 40$

$\sf \longmapsto \: x = \dfrac{40}{5} = 8$

$\sf \bold{x = 8}$

Check:

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

$\sf \longmapsto \dfrac{2(8) - 7}{8 + 4}$

$\sf \longmapsto \dfrac{16 - 7}{12}$

$\sf \longmapsto \dfrac{9}{12} = \dfrac{3}{4}$

∴LHS= RHS (verified)