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Ex.2.5 Q1 Linear Equations in One Variable Solution - NCERT Maths Class 8

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Solve the linear equation \(\begin{align}\frac{x}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4}\end{align}\)

 Video Solution
Linear Equations
Ex 2.5 | Question 1

Text Solution

What is known?


What is unknown?

Value of the variable


Multiple both sides by the L.C.M of the denominators to get rid of fractional number. Now transpose variables to one side and constant to another side.


\[\begin{align}\frac{x}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4}\end{align}\]

LCM of the denominators, \(2, 3, 4,\) and \(5\), is \(60.\)

Multiplying both sides by \(60,\) we obtain

\[\begin{align}60\left( {\frac{x}{2} - \frac{1}{5}} \right) = 60\left( {\frac{x}{3} + \frac{1}{4}} \right)\end{align}\]

Opening the  brackets, we get,
\[\begin{align}30x - 12 &= 20x + 15  \\30x - 20x &= 15 + 12\\10x &= 27\quad \quad \\\,\,\,\,\,x &= \frac{{27}}{{10}}\end{align}\]