Question

How do you solve $7e-4=31$?

Answer 1

Hint: First separate the constants and variables. Bring all the terms containing ‘e’ to the left side of the equation and the constant terms to the right side of the equation. Then do the necessary calculations to obtain the required result.

Complete step-by-step solution:
Solving an equation means we have to find the value of ‘e’ for which the equation gets satisfied, as ‘e’ is the unknown variable of the equation.
The given equation, we have $7e-4=31$
We have to separate the terms containing ‘e’ and the constant terms.
Since, the term containing ‘e’ is already on the left side of the equation so bringing all constant terms to the right side of the equation, we get
$\begin{align}
  & \Rightarrow 7e=31+4 \\
 & \Rightarrow 7e=35 \\
\end{align}$
Dividing both the sides by 7, we get
$\Rightarrow \dfrac{7e}{7}=\dfrac{35}{7}$
Cancelling out 7 both from the numerator and the denominator on the left side and reducing the fraction $\dfrac{35}{7}$ as $\dfrac{35}{7}=\dfrac{5}{1}$ on the right side, we get
$\begin{align}
  & \Rightarrow e=\dfrac{5}{1} \\
 & \Rightarrow e=5 \\
\end{align}$
This is the required solution of the given question.

Note: Separating the constants and variable terms should be the first approach for solving such questions. The fraction $\dfrac{35}{7}$ that we obtained during the calculation can be reduced. As we know the common factor of 35 and 7 is 7, so the greatest common factor of 35 and 7 is 7. Hence dividing the numerator and the denominator of $\dfrac{35}{7}$ by the greatest common factor ‘7’, we get
$\dfrac{35}{7}=\dfrac{35\div 7}{7\div 7}=\dfrac{5}{1}=5$
Hence, the value of ‘x’ we obtained $x=5$.