Solve and check the following equation. \frac{x-7}{5}+\frac{1}{5}

Step 1
An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value and the process of finding the value of the variable is called solving the equation.
The value of the variable for which the equations are equal is known as the solution of the equations and if there are more than one such solution, it is known as the solution set of the equations. Solution is basically the value of the variable for which the equality holds true.
Step 2
${\displaystyle \frac{x-7}{5}+\frac{1}{5}=-\frac{x}{10}}$
Using ${\displaystyle \frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}}$
${\displaystyle \Rightarrow \frac{x-7+1}{5}=-\frac{x}{10}}$
${\displaystyle \Rightarrow \frac{x-6}{5}=-\frac{x}{10}}$
${\displaystyle \Rightarrow x-6=5(-\frac{x}{10})}$
${\displaystyle \Rightarrow x-6=-\frac{x}{2}}$
${\displaystyle \Rightarrow 2(x-6)=-x}$
${\displaystyle \Rightarrow 2x-12=-x}$
${\displaystyle \Rightarrow 2x+x=12}$
${\displaystyle \Rightarrow 3x=12}$
${\displaystyle \Rightarrow x=\frac{12}{3}}$
${\displaystyle x=4}$
Hence, the answer is option A with the answer 4.