Ex.2.5 Q4 Linear Equations in One Variable Solution - NCERT Maths Class 8

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Question

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

Text Solution

What is known?

Equation

What is unknown?

Value of the variable

Reasoning:

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

Steps:

\[\begin{align}\frac{{x - 5}}{3} = \frac{{x - 3}}{5}\end{align}\]

LCM of the denominators, \(3\) and \(5,\) is \(15.\)

Multiplying both sides by \(15,\) we obtain

\[\begin{align}5\left( {x - 5} \right)&= 3\left( {x - 3} \right) \end{align} \]

Opening the brackets we get,

\[\begin{align}5x - 25 &= 3x - 9   \\5x - 3x &= 25 - 9 \\2x &= 16 \\\,\,x& = \frac{{16}}{2} \\\,\,x &= 8 \\\end{align}\]