Answer
$\left \{\frac{45}{7}\right \}$.
Work Step by Step
The given equation is
$\Rightarrow 7[(2x-5)-(x+1)]=(\sqrt7+2)(\sqrt7-2)$
Use the special formula $(A+B)(A-B)=A^2-B^2$
$\Rightarrow 7[2x-5-x-1]=(\sqrt7)^2-(2)^2$
Simplify.
$\Rightarrow 7[x-6]=7-4$
Use the distributive property.
$\Rightarrow 7x-42=3$
Add $42$ to both sides.
$\Rightarrow 7x-42+42=3+42$
Simplify.
$\Rightarrow 7x=45$
Divide both sides by $7$.
$\Rightarrow \frac{7x}{7}=\frac{45}{7}$
Simplify.
$\Rightarrow x=\frac{45}{7}$
The solution set is $\left \{\frac{45}{7}\right \}$.
