Answer
$\{15\}$.
Work Step by Step
Multiply both sides of the given equation by the Least Common Denominator $20$ of all denominators to clear fractions.
$\Rightarrow 20\left( \frac{x-4}{2}-\frac{1}{5} \right)= 20\left( \frac{7x+1}{20} \right)$
Use the distributive property.
$\Rightarrow 20\left( \frac{x-4}{2}\right)-20\left(\frac{1}{5} \right)= 20\left( \frac{7x+1}{20} \right)$
Cancel common factors.
$\Rightarrow 10(x-4)-4(1)= 1\left( 7x+1\right)$
Use the distributive property.
$\Rightarrow 10x-40-4= 7x+1$
Combine like terms.
$\Rightarrow 10x-44= 7x+1$
Add $-7x+44$ to both sides.
$\Rightarrow 10x-44-7x+44= 7x+1-7x+44$
Simplify.
$\Rightarrow 3x= 45$
Divide both sides by $3$.
$\Rightarrow \frac{3x}{3}= \frac{45}{3}$
Simplify.
$\Rightarrow x= 15$
The solution set is $\{15\}$.
