What method can you use if you know the interval containing a solution to an equation?

When you know the interval containing a solution to an equation, the decimal search method is an effective approach. This method involves evaluating the function at various points within the specified interval to narrow down the location of the solution. By systematically testing values, you can identify a point where the function changes sign, indicating the presence of a root between those two values due to the Intermediate Value Theorem, which states that a continuous function will take on every value between its minimum and maximum on a given interval.

This method is particularly useful for equations where finding an exact algebraic solution might be complicated or impossible. It allows for an iterative process that can provide increasingly accurate approximations of the solution by focusing on smaller intervals and honing in on the root.

Using graphical methods may provide visual insights but does not offer the precision that the decimal search method can deliver in determining the exact position of the solution within an interval. Factorization and substitution methods typically are more suited for simpler equations where solutions can be derived algebraically rather than through numerical approximation.