Final answer:
To solve an equation in one variable and express the answer in simplest form, one must perform algebraic manipulations, streamline the process if possible, ensure correct significant figures and units, and review the reasonableness of the solution.
Step-by-step explanation:
When tasked with solving an equation in one variable and expressing the answer in simplest form, we typically will work through a series of algebraic manipulations to isolate the unknown value. This process includes simplifying complex expressions, possibly by recognizing special forms such as perfect squares, and subsequently using algebraic operations to solve for the variable in question.
In some cases, we can streamline this process by combining steps. This might mean performing operations simultaneously on both sides of an equation to more quickly reach the solution. It is also crucial to express answers with the correct number of significant figures and proper units, which ensures precision and relevance to the problem at hand.
At times, it may be necessary to reformat an equation to clarify its components or to express it in terms of direct or indirect proportionalities, which can make it easier to understand or to apply in different contexts.
Finally, once an algebraic solution has been reached, it is important to review the answer and check that it is reasonable given the original problem. This involves scrutinizing for mathematical accuracy and consistency with the given information or equations.