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

Solve and check the following equation.
$\frac{x-7}{5}+\frac{1}{5}=-\frac{x}{10}$
Select the correct choice below and fill in any answer boxes in your choice.
A. The solution set is (_).
B. The solution is the empty set.
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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
$\frac{x-7}{5}+\frac{1}{5}=-\frac{x}{10}$
Using $\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}$
$⇒\frac{x-7+1}{5}=-\frac{x}{10}$
$⇒\frac{x-6}{5}=-\frac{x}{10}$
$⇒x-6=5\left(-\frac{x}{10}\right)$
$⇒x-6=-\frac{x}{2}$
$⇒2\left(x-6\right)=-x$
$⇒2x-12=-x$
$⇒2x+x=12$
$⇒3x=12$
$⇒x=\frac{12}{3}$
$x=4$