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ALGEBRAIC EXPRESSIONS

An algebraic expression combines numbers, variables, and operations to represent a value. Unlike an equation, an expression does not claim that two expressions are equal; it can instead be evaluated, simplified, or rewritten.

Anatomy of an Expression

3CoefficientxVariable+5Constant term

Coefficient

The numerical factor multiplying a variable part. In 3x, the coefficient is 3; in −x, the coefficient is −1.

Variable

A symbol that can stand for an unknown, changing, or generalized value.

Constant Term

A term with no variable factor. Its value does not depend on the variable.

Like Terms

Like terms have the same variable part with the same exponents. Their coefficients may differ, and those coefficients can be combined.

LIKE TERMS
3x + 2x = 5x
NOT LIKE TERMS
3x² + 2x
Expression Lab

Simplification Engine

Set the Value of 'x'2

Unsimplified Expression

3x+4+2x-1
3(2)+4+2(2)-1
6+4+4-1
= 13

Simplified Expression

5x+3
5(2)+3
10+3
= 13
Notice how both sides ALWAYS equal the exact same number, no matter what x is. Simplifying an expression just means doing the math early so there are fewer pieces to plug numbers into later!

Words to Expressions

Verbal relationships can be represented symbolically. Pay attention to order-sensitive phrases such as “less than.”

  • “5 more than a number”x + 5
  • “Twice a number”2x
  • “4 less than a number”x − 4

Reference & Check

Knowledge Check: Expression Structure1 / 3

Which of the following is an EXPRESSION (not an equation)?

Connect Forward

Once two expressions are related by equality, the next question is which values make that equation true.

Next: Solving for X