# Expression vs. Equation: What's the Difference?

Edited by Janet White || By Harlon Moss || Published on November 22, 2023
Expression is a mathematical phrase without an equals sign, whereas equation is a statement showing equality between two expressions.

## Key Differences

Expression and equation are fundamental concepts in mathematics, each with a distinct purpose. An expression can be thought of as a mathematical phrase, representing a particular value or set of values, but it doesn't assert any kind of balance or equality. An equation, on the other hand, serves as a declaration that two expressions are equivalent, meaning they represent the same value.
In arithmetic, an expression might involve numbers, variables, and operations, but it won't make a claim about the relationship between different expressions. An equation, however, will connect two expressions with an equals sign, illustrating that they hold the same value. For instance, "3 + 4" is an expression, but "3 + 4 = 7" is an equation.
In algebra, an expression could be as simple as a single variable or as complex as a polynomial. An equation in algebra often sets an expression equal to another, facilitating the process of solving for unknowns. The utility of equations becomes evident in contexts like system of equations, where multiple equations are used to determine the values of multiple variables.
Broadening the scope beyond mathematics, the term "expression" can also signify a manifestation of feeling, thought, or character. In contrast, "equation" in broader contexts can denote a process of equating one thing with another, suggesting a kind of balance or equivalence between them.

## Comparison Chart

### Definition

A mathematical phrase
A statement of equality between two expressions
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### Includes

Numbers, variables, and operations
Two expressions separated by an equals sign

### Asserts

Value but not equality
Equality between expressions

### Example

5x or 3 + 4
5x = 20 or 3 + 4 = 7

### Broader Meaning

Manifestation of feeling, thought, or character
Equating one thing with another

## Expression and Equation Definitions

#### Expression

A mathematical phrase.
X + 5 is an algebraic expression.
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#### Equation

A mathematical statement showing the equality of two expressions.
2 + 2 = 4 is an equation.

#### Expression

A particular word or phrase.
Raining cats and dogs is an idiomatic expression.

#### Equation

A situation or problem requiring resolution.
The detectives faced a complex equation in the murder mystery.

#### Expression

The process of making one's thoughts known.
Poetry is a form of artistic expression.

#### Equation

A process of equating one thing with another.
His equation of love with sacrifice touched many.

#### Expression

A manifestation of feeling or emotion.
A smile is an expression of happiness.

#### Equation

A formula representing a relationship between variables.
Einstein's E=mc^2 is a famous equation in physics.

#### Expression

A demonstration of a particular quality.
Her painting was an expression of her inner turmoil.

#### Equation

A statement indicating equivalence.
The coach made an equation between hard work and success.

#### Expression

The act of expressing, conveying, or representing in words, art, music, or movement; a manifestation
An expression of rural values.

#### Equation

The act or process of equating or of being equated.

#### Expression

Something that expresses or communicates
Let this plaque serve as an expression of our esteem.

#### Equation

The state of being equal.

#### Equation

(Mathematics) A statement asserting the equality of two expressions, usually written as a linear array of symbols that are separated into left and right sides and joined by an equal sign.

## FAQs

#### Can "5 + 7" be termed an equation?

No, "5 + 7" is an expression; "5 + 7 = 12" is an equation.

#### Is "Raining cats and dogs" an equation?

No, it's an idiomatic expression.

#### What is an expression in mathematics?

An expression is a mathematical phrase without an equals sign.

#### Can "3x" be termed an equation?

No, "3x" is an expression.

#### Are all mathematical phrases with an equals sign equations?

Yes, mathematical statements with an equals sign are equations.

#### In what context might "expression" mean a display of emotion?

In general language, "expression" can refer to showing feelings, like a facial expression.

#### In what scenarios is "equation" used outside mathematics?

It can refer to situations requiring resolution or equating one thing with another.

#### Do expressions always have operations?

No, an expression can be as simple as a single number or variable.

#### How does an equation differ from an expression?

An equation shows equality between two expressions.

#### Can equations have variables?

Yes, equations can have variables, like "x + 3 = 7."

#### What is the primary purpose of an equation in algebra?

To show that two expressions are equivalent and often to solve for unknowns.

#### Can expressions represent a single value?

Yes, an expression like "3x" represents a value, depending on x.

#### Is "E=mc^2" an expression or an equation?

"E=mc^2" is an equation.

#### What does it mean when two expressions are set equal in an equation?

It means they represent the same value.

#### Is "sadness" an expression?

In a broader sense, "sadness" can be felt and shown as an emotional expression.

#### How does an expression become an equation?

By setting it equal to another expression, like turning "x + 2" into "x + 2 = 5."

#### Can an equation be true or false?

Yes, an equation can be true (like 2 + 2 = 4) or false (like 2 + 2 = 5).

#### Why are equations important in mathematics?

Equations establish relationships and allow for problem-solving by setting expressions equal to one another.

#### Can expressions have operations like addition and subtraction?

Yes, expressions can include operations like "a + b" or "c - d."

#### Are equations only restricted to mathematics?

No, equations can also denote situations or the process of equating things in broader contexts.
About Author
Written by
Harlon Moss
Harlon is a seasoned quality moderator and accomplished content writer for Difference Wiki. An alumnus of the prestigious University of California, he earned his degree in Computer Science. Leveraging his academic background, Harlon brings a meticulous and informed perspective to his work, ensuring content accuracy and excellence.
Edited by
Janet White
Janet White has been an esteemed writer and blogger for Difference Wiki. Holding a Master's degree in Science and Medical Journalism from the prestigious Boston University, she has consistently demonstrated her expertise and passion for her field. When she's not immersed in her work, Janet relishes her time exercising, delving into a good book, and cherishing moments with friends and family.