Algebraic Equation — Definition, Formula & Examples
An algebraic equation is a mathematical statement that uses an equals sign to show two expressions are equal, where at least one expression contains a variable (like or ).
An algebraic equation is a statement of equality between two algebraic expressions, containing one or more variables and constants connected by arithmetic operations, for which specific values of the variables make the statement true.
How It Works
To work with an algebraic equation, your goal is usually to find the value of the unknown variable that makes both sides equal. You do this by performing the same operation on both sides — adding, subtracting, multiplying, or dividing — until the variable is isolated. The value you find is called the solution of the equation.
Worked Example
Problem: Solve the algebraic equation .
Step 1: Subtract 5 from both sides to begin isolating .
Step 2: Divide both sides by 2.
Step 3: Check by substituting back into the original equation.
Answer:
Why It Matters
Algebraic equations are the foundation of every algebra course and appear constantly in science, engineering, and finance. Whenever you need to find an unknown quantity — the time for a trip, the cost of an item, or the speed of an object — you set up and solve an algebraic equation.
Common Mistakes
Mistake: Confusing an algebraic expression (like ) with an algebraic equation.
Correction: An equation must have an equals sign. The expression is not an equation, but is.