What is an equation in math?

An equation is a math statement that uses an equals sign to show that two expressions have the same value. It can be checked by calculating each side to see whether they match.

What is equation vs expression?

An equation has an equals sign and compares two sides, such as 4x − 1 = 7. An expression is a math phrase without an equals sign, such as 4x − 1. Only equations can be solved to find values that make them true.

How do you solve a simple equation?

To solve a simple equation, use inverse operations, which are opposite operations, on both sides to keep it balanced. For example, in x + 5 = 12, subtract 5 from both sides to get x = 7, then check by substituting 7 back into the equation.

Can an equation have more than one solution?

Yes. Some equations have one solution, some have none, and some have many. For example, a quadratic equation can have two real solutions, one real solution, or no real solutions, and certain linear equations, like 3x − 6 = 3(x − 2), are true for every value of x.

What Is an Equation? Definition and Examples

How to explain an equation to a child

Think of an equation like a balance scale that is even on both sides. The equals sign means both sides have the same value. Sometimes there is a missing number, and the job is to find the number that makes both sides match. For example, 3 + 2 = 5 is an equation that is true!

Worked examples with equations

Example 1 (younger grades): Simple addition equation

Suppose there are 4 toy cars, and 3 more toy cars are added. This can be written as an equation: 4 + 3 = 7.

The left side is 4 + 3. Add to find 4 + 3 = 7. The right side is 7. Since both sides equal 7, the equation 4 + 3 = 7 is true.

Now consider an equation with a missing number: 5 + □ = 10. Ask, "What number plus 5 equals 10?" Since 5 + 5 = 10, the missing number is 5, so 5 + 5 = 10.

Example 2 (older grades): Linear equation with variables

Consider the equation 2x + 3 = 11, where x is a variable that stands for an unknown number.

Step 1: Subtract 3 from both sides to keep the equation balanced: 2x + 3 − 3 = 11 − 3, so 2x = 8.

Step 2: Divide both sides by 2: 2x ÷ 2 = 8 ÷ 2, so x = 4.

Check the solution by substituting x = 4 into the original equation: 2(4) + 3 = 8 + 3 = 11. Both sides equal 11, so x = 4 is a solution of the equation.

What parents should know about equations

At its core, an equation shows that two expressions, or number sentences, have the same value. The equals sign means "is the same as," not "the answer comes next." A simple equation might be 7 − 2 = 5, while a more complex one might involve variables, such as y = 3x − 1.

Equations are different from expressions. An expression is a math phrase without an equals sign, like 4 + 6 or 3x − 2. An equation always has an equals sign and compares two expressions, such as 4 + 6 = 10 or 3x − 2 = 7.

As your child moves through school, equations are used to model real situations, from sharing pizza slices in elementary school to describing motion, growth, or money in middle and high school.

Going deeper with equations

In algebra, equations often include variables, which are letters that stand for unknown numbers. A linear equation, such as y = mx + b, represents a straight-line relationship between two variables and is also a way to describe a linear function. The graph of such an equation in two variables shows all the pairs (x, y) that make the equation true.

Students learn that linear equations can have one solution, no solution, or many solutions. For example, 2x + 3 = 11 has one solution (x = 4), while 2x + 3 = 2x + 5 has no solution, and 3x − 6 = 3(x − 2) has infinitely many solutions because both sides are always equal.

More advanced work involves quadratic equations (which often have x² terms), exponential and logarithmic equations, and rational or radical equations. These can have two, one, or no real solutions, and sometimes produce extraneous solutions, which are answers that come out of the solving steps but do not actually make the original equation true when checked.

Common mistakes with equations

Treating the equals sign as "the answer comes next" only. A child might see 3 + 4 = 7 + 2 and think it is wrong because "the answer" is not at the end. Correction: Emphasize that the equals sign means both sides must have the same value, so 3 + 4 = 7 and 7 + 2 = 9, which are not equal, so this equation is false.
Mixing up expressions and equations. A student may call 5x + 2 an equation because it has operations. Correction: Explain that an equation must have an equals sign comparing two sides, such as 5x + 2 = 12, while 5x + 2 alone is an expression.
Not doing the same operation to both sides when solving. For the equation 2x + 5 = 11, a student might subtract 5 from the left side only and write 2x = 11, then get x = 5.5, which is incorrect. Correction: Show that to keep the equation balanced, subtract 5 from both sides: 2x + 5 − 5 = 11 − 5, so 2x = 6 and x = 3.

How equations show up in everyday life

Equations appear any time two amounts are compared or balanced. If a game costs $20 and a child has $8 saved each week, the equation 8w = 20 can represent how many weeks, w, are needed to save enough. Recipes, budgets, distances, and scores in games can all be described with equations.

What is an equation?