SAT Question b80d10d7: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice B is correct. Since $\frac{x+5}{x+5}$ is equivalent to $1$, the right-hand side of the given equation can be rewritten as $\frac{x+5}{x+5}-\frac{1}{x+5}$, or $\frac{x+4}{x+5}$. Since the left- and right-hand sides of the equation $\frac{2(x+1)}{x+5}=\frac{x+4}{x+5}$ have the same denominator, it follows that $2(x+1)=x+4$. Applying the distributive property of multiplication to the expression $2(x+1)$ yields $2x+2\times 1$, or $2x+2$. Therefore, $2x+2=x+4$. Subtracting $x$ and $2$ from both sides of this equation yields $x=2$.