1. The problem: Learn the supposition method, a technique used to solve equations by assuming a value for a variable and then verifying or adjusting it. 2. The supposition method involves guessing a value for the unknown variable, substituting it into the equation, and checking if the equation holds true. 3. If the equation is not satisfied, adjust the guess based on the difference and repeat the process until the solution is found. 4. Important rule: The closer the guess is to the actual solution, the fewer iterations are needed. 5. Example: Solve $x + 5 = 12$ using supposition. 6. Step 1: Suppose $x = 4$. 7. Step 2: Substitute into the equation: $4 + 5 = 9$. 8. Step 3: Since $9 \neq 12$, the guess is too low. 9. Step 4: Increase guess, suppose $x = 7$. 10. Step 5: Substitute: $7 + 5 = 12$. 11. Step 6: The equation holds true, so $x = 7$ is the solution. 12. This method is especially useful for complex equations where direct algebraic manipulation is difficult. 13. Summary: Guess, substitute, check, adjust, and repeat until the equation is satisfied.