Question

Solve the following equation. \[\left[ \dfrac{(3x-1)}{5} \right]-\left( \dfrac{x}{7} \right)=3\].

Answer 1

Hint: To solve the linear equation in one variable which is given in the form of a fraction. First, we have to take the LCM and convert the fraction part into the normal form of linear equation in one variable. Then we will simplify both sides of the equation and will take the terms with variables on one side and the constant term on the other side and then we will obtain the result.

Complete step by step answer:
We have to solve the equation, \[\left[ \dfrac{(3x-1)}{5} \right]-\left( \dfrac{x}{7} \right)=3\]
First, we will take the LCM of the equation and then we will further solve our question.
\[\dfrac{7(3x-1)-5x}{35}=3\]
\[\Rightarrow \dfrac{21x-7-5x}{35}=3\]
We will do cross multiplication after that which is as follows.
\[21x-5x-7=105\]
We will take the terms with variable x on one side and the constant terms on the other side.
\[16x=112\]
\[\Rightarrow x=\dfrac{112}{16}\]
\[\begin{align}
  & \Rightarrow x=\dfrac{28}{4} \\
 & \Rightarrow x=7 \\
\end{align}\]
The value of x comes out to be \[7\].
Now we will substitute this value of x in the equation and will check whether the left-hand side is equal to the right-hand side.
So after putting the value of x in the equation, the following result will be obtained.
We will take the left-hand side of the equation which is as follows.
\[\left( \dfrac{3(7)-1}{5} \right)-\left( \dfrac{7}{7} \right)\]
\[\Rightarrow \left( \dfrac{20}{5} \right)-1\]
\[\begin{align}
  & \Rightarrow 4-1 \\
 & \Rightarrow 3 \\
\end{align}\]
So the left-hand side becomes equal to the right-hand side and hence our answer is correct.

Note:
There are three methods to solve linear equations in one variable.
1. Trial and Error.
2. Inverse operations.
3. Transposition Method.