Definition
Equation
An equation is a mathematical statement that says two expressions have the same value.
What it means
The equals sign is a balance sign: the left side and the right side must be worth the same amount. An equation can show a fact, such as 6 + 1 = 7, or ask which value makes a statement true, such as x + 3 = 8. It is not an instruction that says “write the answer next.”
Remember it
Read “=” as “has the same value as” in both directions.
Example
For 2n + 1 = 11, try n = 5. The left side becomes 2 × 5 + 1 = 11, which matches the right side. Therefore 5 is a solution of the equation.
Watch for
3 + 4 is an expression, not an equation, because it does not make an equality claim.
Common mix-up
The equals sign does not mean “the answer comes next”; it states that both sides have the same value.
Exact meaning
An equation is a mathematical statement asserting that the expression on one side of an equals sign has the same value as the expression on the other side. An equation may be true, false, or true only for particular values of its variables.