SAT Question 1f0966db: Linear Functions answer and explanation with Desmos solution

Substituting $5$ for $f\left(x\right)$ in the given function yields $5=\frac{9}{7}x+\frac{8}{7}$. Multiplying each side of this equation by $7$ yields $7\left(5\right)=7\left(\frac{9}{7}x+\frac{8}{7}\right)$, or $35=9x+8$. Subtracting $8$ from each side of this equation yields $27=9x$. Dividing each side of this equation by $9$ yields $3=x$. Therefore, $f\left(x\right)=5$ when the value of $x$ is $3$.