How to Identify Expressions and Equations?

A step-by-step guide to identifying expressions and equations

An expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division. Expressions do not contain an equal sign and cannot be solved for a specific value. For example, \(2x + 3\) is an expression.

An equation, on the other hand, is a mathematical statement that states that two expressions are equal. Equations contain an equal sign \((=)\) and can be solved for a specific value. For example, \(2x + 3 = 7\) is an equation.

To identify an expression, look for a mathematical phrase that does not contain an equal sign. To identify an equation, look for a mathematical statement that contains an equal sign.

It is also important to note that an equation can be written in different forms, such as a verbal form, an algebraic form, and a graphical form. As an example, the verbal form of the equation is “Five more than a number is equal to nine.” This can be written in algebraic form as \(x+5=9\), and the graphical form can be represented by a line in a coordinate plane.

It’s essential to be able to identify expressions and equations, as they are the building blocks of algebra and other branches of mathematics. Understanding the distinction between the two will help you to solve problems and understand mathematical concepts more effectively.

Identifying Expressions and Equations -Example 1

Is this an expression or an equation?
\(8×(6-2)=32\)
Solution:
It has an equal sign, so it is an equation.

Identifying Expressions and Equations -Example 2

Is this an expression or an equation?
\(51+3\;w\)
Solution:
It has no equal sign so; it is an expression.

Exercises for Identifying Expressions and Equations

Determine if each is an expression or an equation.

1. \(\color{blue}{16-10=6}\)
2. \(\color{blue}{y+9=40}\)
3. \(\color{blue}{\frac{x}{25}}\)
4. \(\color{blue}{x+5y\:-\:10}\)

1. \(\color{blue}{\:equation}\)
2. \(\color{blue}{\:equation}\)
3. \(\color{blue}{expression}\)
4. \(\color{blue}{expression}\)