Question

How do you solve the linear equation $2\dfrac{j}{7}-\dfrac{1}{7}=\dfrac{3}{14}$ ?

Answer 1

Hint: We have been given an equation in fractional format. The constant term as well as the term of variable-j is in fractions. We shall start by simplifying the equation given to us by dividing 7 from denominators of both sides of the equation. Then we shall cross multiply the terms on the left hand side and right hand to solve the equation further.

Complete step by step solution:
Given that $2\dfrac{j}{7}-\dfrac{1}{7}=\dfrac{3}{14}$. In order to obtain the solution of this equation, we shall find out the value of variable-j.
We see that 7 is a common factor present in both the terms on the left hand side of the equation as well as on the right hand side of the equation as $7\times 2=14$. Thus, we shall cancel 7 from the equation.
$\Rightarrow \dfrac{2j}{1}-\dfrac{1}{1}=\dfrac{3}{2}$
$\Rightarrow 2j-1=\dfrac{3}{2}$
Transposing the constant term 1 to the right hand side, we get
$\Rightarrow 2j=\dfrac{3}{2}+1$
$\Rightarrow 2j=\dfrac{5}{2}$
Since there are no terms to be transposed from left hand side to right hand side of the equation or vice-versa, thus, we will divide both sides by 2 to make the coefficient of j equal to 1.
$\Rightarrow j=\dfrac{5}{4}$
Thus, we have obtained the value of j equal to $\dfrac{5}{4}$.
Therefore, the solution of $2\dfrac{j}{7}-\dfrac{1}{7}=\dfrac{3}{14}$ is $j=\dfrac{5}{4}$.

Note: If we fail to notice the common factors present in the equation and do not divide the equation by 7 then the calculations of the linear equation would become lengthier which would further make the equation complex. Thus, we must be observant enough to notice and cancel the common factors in the equation.