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An equation is a mathematical statement that shows the relationship between two or more quantities. It usually contains variables, constants, and mathematical operations, and the goal is to find the value of the unknown variable(s).
The process for solving an equation involves isolating the variable on one side of the equation by using inverse operations. This means that you perform the opposite mathematical operation on both sides of the equation until the variable is alone on one side. The value that makes the equation true is the solution.
Inverse operations are mathematical operations that undo each other. For example, addition and subtraction are inverse operations, as well as multiplication and division. Using inverse operations is essential when solving equations because they allow you to isolate the variable.
The order of operations, also known as PEMDAS, is a set of rules that determine the order in which mathematical operations should be performed. It stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Following the order of operations is crucial when solving equations to get the correct solution.
If there are variables on both sides of the equation, the first step is to combine like terms on each side. Next, use inverse operations to isolate the variable on one side of the equation. Finally, solve for the variable by using the order of operations. If necessary, check your solution by plugging it back into the original equation.