Question

Solve x/3 + 1/5 = x/2 – 1/4

Answer 1

$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; Solution :-}}}$

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf\textcolor{orange}{ \cfrac{\large\textsf{x}}{\large\textsf{3}} + \cfrac{\large\textsf{1}}{\large\textsf{5}} = \cfrac{\large\textsf{x}}{\large\textsf{2}} - \cfrac{\large\textsf{1}}{\large\textsf{4}} }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ \cfrac{\large\textsf{5x + 3}}{\large\textsf{3 × 5}} =\cfrac{\large\textsf{4x - 2}}{\large\textsf{2 × 4}} }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ \cfrac{\large\textsf{5x + 3}}{\large\textsf{15}} = \cfrac{\large\textsf{4x - 2}}{\large\textsf{8}} }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{8 ( 5x + 3 ) = ( 4x - 2 ) 15}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{40x + 24 = 60x - 30}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{40x - 60x = -30 - 24}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{- 20x = - 54}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ x = \cancel\cfrac{\large\textsf{- 54}}{\large\textsf{- 20}} }\\\\\\\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{ x =\; \cfrac{\large\textsf{27}}{\large\textsf{10}} }}$