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What's the Difference Between Expressions and Equations?

expressions and equations: girl solving a math problem

Expressions and equations are terms you've probably heard in real-life, most often in a high school math class. But do you know the real difference? They both can have numbers and variables, but there’s one key difference. Let's explore what this is and show you how to simplify and evaluate expressions and equations.

What's the Difference Between Expressions and Equations?

An algebraic expression involves numbers, variables, or a combination of both. As you can see in the following expressions, there is one element from equations that are missing here:

expressions and equations: sample of expressions

There are no equal signs! This is what makes writing expressions different from writing equations.

Both equations and expressions can have variables, coefficients , whole numbers, decimals, exponents, addition, subtraction, multiplication and division. But unlike expressions, algebraic equations must always include an equal sign:

algebraic expressions and equations

As you can see in the simple equations above, there are two sides of the equation: a right and a left side. So technically, an equation is made of two expressions. The equal sign establishes the two sides of the equation as equivalent expressions.

Now that we know the difference between expressions and equations, let's learn how to simplify them.

Simplifying Expressions and Equations

Simplifying an equation means rewriting the expressions so you can solve for the value of the variable in question.

Below is a multi-step equation. It’s made of two expressions joined by an equal sign.

Solving equations like this starts by using order of operations. In this case, we’ll multiply the values and variables inside the parentheses by the numbers outside them:

expressions and equations: multi-step equation

The next step to simplifying this mathematical expression is to combine the like terms. To do this, we’ll first move like terms on the same sides of the equal sign.

combining like terms

Our next move is combining like terms by subtracting the values connected to our variable, x. We’ll also add the numbers not connected to a variable.

subtracting values connected to the variable

Now that we've simplified this equation, there is only one step left. To get x on its own, we need to find the quotient that results from dividing 52 by -2:

finding the quotient

Understanding Expressions and Equations

You can define a numerical expression as a group of numbers and variables with no equal sign. An equation is a group of numbers and variables that does include an equal sign.

Once you understand these definitions, you can recognize that an equation is simply two expressions joined together by an equal sign. And, you can simplify equations and write expressions and equations.

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