Question

solve this equation​

Answer 1

       $\text{\huge \underline{Answer:}}$

       $\text{The given equation is:}$

       $\dfrac{t}{2} + \dfrac{t-2}{3} = \dfrac{4 + t}{5}$

       $\text{Taking LCM on L.H.S and simplifying...}$

$\implies \dfrac{3t}{6} + \dfrac{2(t-2)}{6} = \dfrac{4 + t}{5}$

$\implies \dfrac{3t+2(t-2)}{6} = \dfrac{4 + t}{5}$

$\implies \dfrac{3t+2t-4}{6} = \dfrac{4 + t}{5}$

$\implies \dfrac{5t-4}{6} = \dfrac{4 + t}{5}$

       $\text{Cross multiplying..}$

$\implies 5(5t-4) = 6(4 + t)$

$\implies 25t-20 = 24 + 6t$

$\implies 25t-20 - 24 - 6t = 0$

$\implies 19t - 44 = 0$

$\implies 19t = 44$

$\implies \boxed{\boxed{t = \dfrac{44}{19}}}$

Answer 2

$\huge\mathcal{\fcolorbox{aqua}{azure}{\red{❖Solution}}}$

$\large\blue{\sf{We~have,}}$

$\frac{3t + 2t - 4}{6} = \frac{4 + t}{5}$

$\frac {5t - 4}{6} = \frac{4 + t}{5}$

$\large\blue{\sf{By~the~method~of~cross~multiplication}}$

$\large\blue{\sf{5~(5t-4)~=~6~(4+t)~}}$

$\large\blue{\sf{25t~-~20~=~24~+~6t}}$

$\large\blue{\sf{19t~=~44}}$

$\large\orange{\sf{t~=~\frac{44}{9}~}}$