1. **State the problem:** Solve the linear equation $4x + 9 = 25$ for $x$. 2. **Isolate the variable term:** Subtract 9 from both sides to get rid of the constant on the left. $$4x + 9 - 9 = 25 - 9$$ $$4x = 16$$ 3. **Solve for $x$:** Divide both sides by 4 to isolate $x$. $$\frac{\cancel{4}x}{\cancel{4}} = \frac{16}{4}$$ $$x = 4$$ 4. **Final answer:** The solution to the equation is $x = 4$. This means when $x$ is 4, the original equation $4x + 9 = 25$ holds true.