Expressions and Equations

Grade 6 · Math · Study Guide

Learn how to write, evaluate, and solve algebraic expressions and one-variable equations.

An expression is a mathematical phrase that contains numbers, variables, and operations — but no equals sign. For example, 3x + 5 is an expression. An equation, on the other hand, shows that two expressions are equal, like 3x + 5 = 20.

Variables are letters that represent unknown values. When you evaluate an expression, you substitute a number for the variable and calculate the result. For example, if x = 4, then 3x + 5 = 3(4) + 5 = 17.

To solve an equation, you find the value of the variable that makes the equation true. Use inverse operations to isolate the variable. Inverse operations undo each other: addition undoes subtraction, and multiplication undoes division. Whatever you do to one side of the equation, you must do to the other side to keep it balanced.

For example, to solve x + 7 = 15, subtract 7 from both sides: x = 8. To solve 4x = 28, divide both sides by 4: x = 7.

Expressions can also be written from real-world situations. If a bag has n apples and you add 3 more, the expression is n + 3. Writing expressions from words is an important skill that connects math to everyday life.

Key terms

Variable
A letter that represents an unknown number in an expression or equation
Expression
A mathematical phrase with numbers, variables, and operations but no equals sign
Equation
A mathematical statement showing two expressions are equal, using an equals sign
Evaluate
To find the value of an expression by substituting a number for the variable
Inverse Operations
Operations that undo each other, such as addition and subtraction or multiplication and division
Solution
The value of the variable that makes an equation true

Flashcards

Evaluate 2x + 1 when x = 5
2(5) + 1 = 11
Solve: x + 8 = 15
x = 7 (subtract 8 from both sides)
Solve: 3x = 21
x = 7 (divide both sides by 3)
Expression vs. Equation
Expression has no equals sign; equation has an equals sign
Inverse of multiplication
Division
Write an expression: 7 more than n
n + 7
Solve: x − 4 = 10
x = 14 (add 4 to both sides)
What does it mean to substitute?
Replace the variable with a specific number to calculate the value

Questions

  1. What is the value of 5x − 3 when x = 4?

    1. 13
    2. 17
    3. 12
    4. 22
    Show answer

    Answer: 17

    5(4) − 3 = 20 − 3 = 17

  2. An expression always contains an equals sign.

    Show answer

    Answer: False

    An expression does not have an equals sign; only equations do

  3. If 2x + 6 = 14, then x = ___.

    Show answer

    Answer: 4

    2x + 6 = 14 → 2x = 8 → x = 4

  4. Which of the following is an equation?

    1. 4n + 2
    2. 3y − 7 = 11
    3. 6 + x
    4. 2(a + 5)
    Show answer

    Answer: 3y − 7 = 11

    3y − 7 = 11 contains an equals sign, making it an equation

  5. To solve x − 9 = 3, you add 9 to both sides.

    Show answer

    Answer: True

    Adding 9 to both sides isolates x: x = 12

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