Question

1/2(2x-6) = 1/4(8-12x)​

Answer 1

$\sf \frac{1}{2} (2x - 6) = \frac{1}{4} (8 - 12x) \\ \\ \sf \: cross \: \: multiplying \: \: \frac{1}{2} \: \: and \: \: \frac{1}{4} \\ \\ \sf \: 4(2x - 6) = 2(8 - 12x) \\ \\ \sf \: 8x - 24 = 16 - 24x \\ \\ \sf \: 8x + 24x = 16 + 24 \\ \\ \sf \: 32x = 40 \\ \\ \sf \: x = \frac{40}{32} \\ \\ \red{ \sf \: x = \frac{5}{4}}$

I HOPE IT HELPS.

Answer 2

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

$\sf \longmapsto \dfrac{1}{2} (2 x- 6) = \dfrac{1}{4} (8 - 12x)$

$\sf \longmapsto \dfrac{2x - 6}{2} = \dfrac{8 - 12x}{4}$

Now,cross multiply to both sides:

$\sf \longmapsto4(2x - 6) = 2(8 - 12x)$

$\sf \longmapsto8x - 24 = 16 - 24x$

$\sf \longmapsto8x + 24x = 16 + 24$

$\sf \longmapsto32x = 40$

$\sf \longmapsto \: x = \dfrac{40}{32} = { \bold{ \dfrac{5}{4} }}$

Check:

$\sf \longmapsto\large \dfrac{1}{2} (2x - 6) = \dfrac{1}{4} (8 - 12x)$

$\sf \longmapsto\large \dfrac{1}{2} (2 \times \frac{5}{4} - 6) = \dfrac{1}{4} (8 - 12 \times \frac{5}{4} )$

$\sf \longmapsto \large\dfrac{1}{2} ( \frac{10}{4} - 6) = \dfrac{1}{4} (8 - \frac{60}{4} )$

$\sf \longmapsto \large\dfrac{1}{2} ( \frac{10 - 24}{4} ) = \dfrac{1}{4} (8 - 15)$

$\sf \longmapsto\large \dfrac{1}{ \cancel{{2}}} ( \frac{ { \cancel{- 14}}}{4} ) = \dfrac{1}{4} ( - 7)$

$\sf \longmapsto\large - \dfrac{7}{4} = - \dfrac{7}{4}$

Therefore,LHS=RHS (verified)