Question

2(t+1)/3 - t-2/4 = t/2 + 1/2​

Answer 1

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

$\sf \longmapsto \dfrac{2(t + 1)}{3} - \dfrac{t - 2}{4} = \dfrac{t}{2} + \dfrac{1}{2}$

Taking LCM both sides :

LCM of 3 & 4 is 12

$\sf \longmapsto \dfrac{4(2t + 2) - 3(t - 2)}{12} = \dfrac{t + 1}{2}$

$\sf \longmapsto \dfrac{8t + 8 - 3t + 6}{12} = \dfrac{t + 1}{2}$

Now,cross multiply to both sides:

$\sf \longmapsto2(8t - 3t + 8 + 6) = 12(t + 1)$

$\sf \longmapsto2(5t + 14) = 12(t + 1)$

$\sf \longmapsto10t + 28 = 12t + 12$

$\sf \longmapsto28 - 12 = 12t - 10t$

$\sf \longmapsto16 = 2t$

$\sf \longmapsto \:t = 16 \div 2 = 8$

$\sf\large \boxed{ \bold{t = 8}}$

Check:

$\sf \longmapsto2(5t + 14) = 12(t + 1)$

$\sf \longmapsto 2(5 \times 8 + 14)$

$\sf \longmapsto2(40 + 14)$

$\sf \longmapsto2(54) = 108$

Taking RHS

$\sf \longmapsto12(t + 1)$

$\sf \longmapsto12(8 + 1)$

$\sf \longmapsto12 \times 9 = 108$

LHS=RHS(Verified)