1. **State the problem:** Solve the linear equation $8 + 9x = 53$ for $x$. 2. **Isolate the variable term:** Subtract 8 from both sides to get the term with $x$ alone on one side. $$8 + 9x = 53$$ $$\cancel{8} + 9x = 53 - \cancel{8}$$ $$9x = 45$$ 3. **Solve for $x$:** Divide both sides by 9 to isolate $x$. $$\frac{9x}{\cancel{9}} = \frac{45}{\cancel{9}}$$ $$x = 5$$ 4. **Conclusion:** The solution to the equation $8 + 9x = 53$ is $x = 5$. This means when $x$ is 5, the equation balances correctly.