Understanding Algebraic Expressions

Grade 7 · Math · Study Guide

Learn to read, write, and simplify algebraic expressions using variables, coefficients, and operations.

An algebraic expression is a mathematical phrase that uses numbers, variables (letters that stand for unknown values), and operations like addition, subtraction, multiplication, and division. For example, 3x + 7 is an expression where 3 is the coefficient, x is the variable, and 7 is a constant.

Expressions are made up of terms. In 4x² - 2x + 9, there are three terms: 4x², -2x, and 9. Terms with the same variable and exponent are called like terms, and they can be combined. For example, 5x + 3x = 8x, but 5x + 3x² cannot be simplified because the exponents differ.

Evaluating an expression means substituting a number in for the variable and computing the result. If x = 4, then 3x + 7 becomes 3(4) + 7 = 12 + 7 = 19. Algebraic expressions are the building blocks of equations and form the foundation of all higher mathematics — from geometry to calculus.

Key terms

Variable
A letter (like x or y) that represents an unknown or changing value.
Coefficient
The number multiplied by the variable in a term (the 3 in 3x).
Constant
A fixed number in an expression with no variable attached.
Like Terms
Terms that have the same variable raised to the same power and can be combined.
Evaluate
To find the value of an expression by substituting a number for the variable.

Flashcards

Variable
A letter standing for an unknown value (e.g., x, y, n).
Coefficient
The number multiplied by the variable — in 7y, the coefficient is 7.
Constant
A plain number in an expression with no variable (e.g., the 4 in 3x + 4).
Term
A single number, variable, or product of both separated by + or – signs.
Like Terms
Terms with the same variable and exponent that can be added or subtracted.
Expression
A math phrase with numbers, variables, and operations — but no equals sign.
Evaluate
Plug a number in for the variable and compute the result.
Simplify
Combine like terms to write an expression in its most compact form.

Questions

  1. In the expression 5x + 3, what is the coefficient?

    1. 3
    2. x
    3. 5
    4. 8
    Show answer

    Answer: 5

    The coefficient is the number in front of the variable. In 5x + 3, the coefficient of x is 5.

  2. The terms 4x and 4x² are like terms and can be combined.

    Show answer

    Answer: False

    Like terms must have the same variable AND the same exponent. 4x and 4x² have different exponents, so they cannot be combined.

  3. If x = 3, the value of 2x + 5 is ___.

    Show answer

    Answer: 11

    Substitute x = 3: 2(3) + 5 = 6 + 5 = 11.

  4. Which expression has exactly 3 terms?

    1. 7x
    2. 2x + 5
    3. 4x² - 3x + 1
    4. 6 + 2
    Show answer

    Answer: 4x² - 3x + 1

    4x² - 3x + 1 has three separate terms: 4x², -3x, and 1.

  5. Simplify: 6x + 2x - 3

    1. 8x - 3
    2. 5x
    3. 8x + 3
    4. 6x - 1
    Show answer

    Answer: 8x - 3

    Combine the like terms first: 6x + 2x = 8x. The constant -3 stays, giving 8x - 3.

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