# 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?

Video Solution
Linear Equations
Ex 2.2 | Question 13

## 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}

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