1. **State the problem:** Solve the equation $2^x + x = 5$ for $x$. 2. **Understand the equation:** This is a transcendental equation involving both an exponential term $2^x$ and a linear term $x$. There is no simple algebraic formula to isolate $x$. 3. **Approach:** We can try to find the solution by inspection or numerical methods. Let's check some values: - For $x=1$, $2^1 + 1 = 2 + 1 = 3$ (less than 5). - For $x=2$, $2^2 + 2 = 4 + 2 = 6$ (greater than 5). 4. Since the function $f(x) = 2^x + x$ is continuous and increasing, the solution lies between 1 and 2. 5. Try $x=1.5$: $2^{1.5} + 1.5 = \sqrt{2^3} + 1.5 = \sqrt{8} + 1.5 \approx 2.828 + 1.5 = 4.328$ (less than 5). 6. Try $x=1.7$: $2^{1.7} + 1.7 \approx 3.249 + 1.7 = 4.949$ (still less than 5). 7. Try $x=1.75$: $2^{1.75} + 1.75 \approx 3.363 + 1.75 = 5.113$ (greater than 5). 8. The solution is between 1.7 and 1.75. By linear interpolation: $$x \approx 1.7 + \frac{5 - 4.949}{5.113 - 4.949} \times (1.75 - 1.7) = 1.7 + \frac{0.051}{0.164} \times 0.05 \approx 1.7 + 0.0155 = 1.7155$$ 9. **Final answer:** $x \approx 1.72$ (rounded to two decimal places).