1. Stating the problem: We need to find the value of $x$ such that $f(x) = 19$ for the function $f(x) = 2x + 3$. 2. Write the equation: $$2x + 3 = 19$$ 3. Subtract 3 from both sides to isolate the term with $x$: $$2x + \cancel{3} - \cancel{3} = 19 - 3$$ $$2x = 16$$ 4. Divide both sides by 2 to solve for $x$: $$\frac{2x}{\cancel{2}} = \frac{16}{\cancel{2}}$$ $$x = 8$$ 5. Final answer: The value of $x$ for which $f(x) = 19$ is $x = 8$.