Question

How do you solve $ \dfrac{n}{n-3}=\dfrac{2}{3} $ ?

Answer 1

Hint: In this question, we need to solve an equation in terms of n to find the value of n which satisfies the equation. For this, we will first cross multiply the equation to have a variable in the numerator only. After that, we will add, subtract, multiply and divide some terms into both sides of the equation such that we are left with the variable n on one side of the equation and a constant on the other side of the equation. The value of the constant will be the required value of n which satisfies this equation.

Complete step by step answer:
Here we are given an equation as $ \dfrac{n}{n-3}=\dfrac{2}{3} $ .
We need to solve it to find the value of n which satisfies the equation.
For this, we need to change the equation in the form n = c where c is constant.
Let us first cross multiply the equation i.e. multiply denominator left side to the right sides numerator and right sides denominator with left sides numerator we get \[n\times 3=2\times \left( n-3 \right)\].
The left side of the equation can be written as n having coefficient 3 and let us multiply 2 by both n and 3 inside the bracket we get $ 3n=2n-6 $ .
We see that the variable 2n is not required on the right side of the equation so let us remove it by subtracting 2n from both sides of the equation we get $ 3n-2n=2n-6-2n $ .
Subtracting the like terms on both sides of the equation we get $ n=-6 $ .
This equation is of the form n = c. Therefore the required value of n is -6 which will satisfy the equation.

Note:
 Students should take care of signs while adding, subtracting the terms. Students can make mistakes of forgetting to multiply 2 by both n and -3. They can check their answer in the following way,
Putting value of n as -6 in $ \dfrac{n}{n-3}=\dfrac{2}{3} $ we get $ \dfrac{-6}{-6-3}=\dfrac{2}{3} $ .
Simplifying the denominator on the left side we get $ \dfrac{-6}{-9}=\dfrac{2}{3} $ .
Dividing the numerator and the denominator by -3 on the left side of the equation we get $ \dfrac{-6}{-9}\div \dfrac{-3}{-3}=\dfrac{2}{3} $ .
Simplifying we get $ \dfrac{2}{3}=\dfrac{2}{3} $ .
The left side is equal to the right side. So the value of n as -6 is the correct answer.