What is an algebraic equation?
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An algebraic equation is a mathematical statement that uses variables, numbers, and mathematical operations to express the equality of two expressions. It is commonly written in the form "expression = expression" or "expression - expression = 0". The purpose of an algebraic equation is to find the value or values of the variables that make the equation true.
To understand and solve algebraic equations, you can follow these steps:
1. Identify the variables: Variables are usually represented by letters such as x, y, or a. Determine which quantities are unknown and assign variables to them.
2. Determine the operations: Look for the mathematical operations involved in the equation, such as addition, subtraction, multiplication, division, or exponentiation.
3. Simplify the equation: Use the order of operations (PEMDAS/BODMAS) to simplify the expressions on both sides of the equation. Combine like terms and perform any necessary operations.
4. Isolate the variable: The goal is to get the variable on one side of the equation and the constants on the other side. Use inverse operations to undo the operations on the variable. For example, if the variable is multiplied by 3, divide both sides by 3.
5. Solve for the variable: After isolating the variable, you will end up with an equation that states the value of the variable. Solve the equation to find the value or values that satisfy the equation.
6. Check your answer: Substitute the found value(s) back into the original equation to verify if it satisfies the equation. If it does, then you have successfully solved the algebraic equation.
Remember, the key to solving algebraic equations is to perform the same operation on both sides of the equation to maintain equality.