# Ex.2.5 Q6 Linear Equations in One Variable Solution - NCERT Maths Class 8

## Question

Solve the linear equation \(\begin{align}m - \frac{{m - 1}}{2} = 1 - \frac{{m - 2}}{3}\end{align}\)

## 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:**

LCM of the denominators, \(2\) and \(3,\) is \(6.\)

Multiplying both sides by \(6,\) we obtain

\[\begin{align}6m \! - \! 3\left( {m\! -\! 1} \right) & \! = \! 6 \!-\! 2\left( {m \! - \! 2} \right)\\6m \! - \! 3m \! + \! 3 & \! = \! 6 \! - \! 2m \! + \! 4 \\\quad\quad\quad\text{(Opening }& \text{the brackets)}\\6m\! -\! 3m \! + \! 2m & \! = \! 6 \! + \! 4 \! - \! 3\\5m & \! = \! 7\\\,\,m & \! = \! \frac{7}{5}\end{align}\]