Final answer:
There are three types of answers when solving equations with variables on both sides: a unique solution, multiple solutions, or no solution at all. This involves identifying unknowns and knowns, choosing the right equation or system of equations, and solving step by step.
Step-by-step explanation:
When solving equations with variables on both sides, three types of answers are possible. The first type of solution is where there is one specific answer for the variable, meaning that after simplifying the equation, you get a unique value for the variable. The second possibility is that there are multiple solutions to the equation, which usually occurs when the variable is squared, leading to two potential solutions. Finally, there is the chance that the equation has no solution, which happens when the variables cancel each other out, and you are left with a false statement such as 0 = 3.
To solve such equations, first identify the unknowns and the knowns. Then choose an appropriate equation that will help solve for the unknowns. This may require you to use just one equation or a system of equations, depending on the complexity of the problem. If there are multiple unknowns, multiple equations will likely be necessary. It’s important to solve the equations carefully, step by step, to find the unknown values.