Question

Solve the following linear equation
x/2_1/5=x/3+1/4
​

Answer 1

Hope this answer helps you

Answer 2

$\red{ \huge{ \underline{ \overline {\mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{ \mid}}}}}}}}$

$\bold{ \: \: \: \: \: \: \: \: \: \: \frac{x}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4} } \\ \\ \bold{ \Longrightarrow \: \frac{5x - 2}{10} = \frac{4x + 3}{12} }$

$\underline{ \underline{ \bold{ \: \: By \: \: Cross \: \: Multiplication \: \: }}}$

$\bold{ \frac{5x - 2}{10} = \frac{4x + 3}{12} } \\ \\ \bold{ \Longrightarrow \: 12(5x - 2) = 10(4x + 3)} \\ \\ \bold{ \Longrightarrow \: 60x - 24 = 40x + 30} \\ \\ \bold{ \Longrightarrow \: 60x - 40x = 30 + 24} \\ \\ \bold{ \Longrightarrow \: 20x = 54} \\ \\ \bold{ \Longrightarrow \: x= \frac{54}{20} } \\ \\ \bold{ \therefore \: \: \boxed{ \bold{x = \frac{27}{10} }}}$

$\red{ \huge{ \underline{ \overline {\mid{ \bold{ \purple{ \: \: VERIFICATION\: \: \red{ \mid}}}}}}}}$

$\underline{ \bold{ \: \: Putting \: \: the \: \: value \: \: of \: \: \red{x} \: \: in \: \: L.H.S. \: \: }} \\ \underline{\bold{ \: \: of \: \: the \: \:equation \: \: }}$

$\bold{L.H.S. = \frac{x}{2} - \frac{1}{5} } \\ \\ \bold{ = \frac{ \frac{27}{10} }{2} - \frac{1}{5} } \\ \\ \bold{ = (\frac{27}{10} \times \frac{1}{2}) - \frac{1}{5} } \\ \\ \bold{ = \frac{27}{20} - \frac{1}{5} } \\ \\ \bold{ = \frac{27 - 4}{20} } \\ \\ \bold{ = \frac{23}{20} }$

$\underline{ \bold{ \: \: Putting \: \: the \: \: value \: \: of \: \: \red{x} \: \: in \: \: R.H.S.\: \: }} \\ \underline{\bold{ \: \: of \: \: the \: \:equation \: \: }}$

$\bold{R.H.S. = \frac{x}{3} + \frac{1}{4} } \\ \\ \bold{ = \frac{ \frac{27}{10} }{3} + \frac{1}{4} } \\ \\ \bold{ = (\frac{27}{10} \times \frac{1}{3} ) + \frac{1}{4} } \\ \\ \bold{ = \frac{27}{30} + \frac{1}{4} } \\ \\ \bold{ = \frac{54 + 15}{60} } \\ \\ \bold{ = \frac{69}{60} } \\ \\ \bold{ = \frac{23}{20} }$

$\bold{ \therefore \: \: \underline{ \: \: \: L.H.S. = R.H.S. \: \: \: }}$