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

## Question

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

## Text Solution

**What is known?**

Equation

**What is unknown?**

Value of the variable

**Reasoning: **

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.

**Steps:**

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

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,

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