# EX.2.2 Q13 Linear Equations in One Variable Solutions - NCERT Maths Class 8

## Question

A rational number is such that when you multiply it by \(\begin{align}\frac{5}{2}\end{align}\) and add \(\begin{align}\frac{2}{3}\end{align}\)to the product, you get \(\begin{align}\frac{-7}{12}\end{align}\). What is the number?

## Text Solution

**What is known?**

A rational number is such that when multiply it by\(\begin{align}\frac{5}{2}\end{align}\) and add\(\begin{align}\frac{2}{3}\end{align}\) to the product, answer is \(\begin{align}\frac{-7}{12}\end{align}\).

**What is unknown?**

Numbers.

**Reasoning:**

Assume the rational number to be a variable. Apply the conditions sequentially to form a linear equation.

**Steps:**

Let the rational number be \(x\)

Multiply by \(\begin{align}\frac{5}{2} \to x \times \frac{5}{2} = \frac{{5x}}{2}\end{align}\)

Add \(\begin{align}\frac{2}{3}\end{align}\)in the product \(\begin{align}= \frac{{5x}}{2} + \frac{2}{3}\end{align}\)

Answer is \(\begin{align}➔ \frac{{ - 7}}{{12}}\end{align}\)

\[\begin{align} \therefore \quad \frac{{5x}}{2} + \frac{2}{3} &= \frac{{ - 7}}{{12}}\\\frac{{5x}}{2} &= \frac{{ - 7}}{{12}} - \frac{2}{3}\\\frac{{5x}}{2} &= \frac{{ - 7 - 8}}{{12}}\\\frac{{5x}}{2} &= \frac{{ - 15}}{{12}}\\x &= \frac{{ - 15}}{{12}} \times \frac{2}{5}\\x &= \frac{{ - 3}}{6}\\x &= \frac{{ - 1}}{2}\end{align}\]

The number is \(\begin{align}- \frac{1}{2}.\end{align}\)