Final answer:
The rule to solve equations involves reversing the order of operations applied to the variable, identifying knowns, solving for unknowns, substituting known values, and verifying the solution's reasonableness.
Step-by-step explanation:
The rule to solve both linear and non-linear equations is to identify what is being done to the variable and do the order of operations backwards. This means, first, make a list of what is given or can be inferred from the problem (identify the knowns). Then, solve the appropriate equation or equations for the quantity to be determined (the unknown). This often requires manipulating one or more equations to give you the desired answer. A translational analog can be helpful for conceptual understanding if you are familiar with such motion.
After finding the appropriate equation, substitute the known values along with their units into the equation, and solve to obtain numerical solutions complete with units. For angle measurements, be sure to use units of radians. Finally, check your answer to ensure that it makes sense in the context of the problem, looking at the reasonableness of the numbers and correctness of the units.
When dealing with operations and equations, remember that multiplication or division by the same number on both sides of an equation does not change equality. Moreover, when inverting a mathematical function, such as taking the square root in the Pythagorean theorem to find the length of a side, ensure that you apply the correct inverse operation to obtain the desired variable.