Grade 7 · Free math lesson
Pre-Algebra
After this lesson, you will be able to read, write, and simplify basic algebra expressions using numbers and variables.
Practice Pre-Algebra freeSkills in this unit
Pick a skill to try three free questions on just that.
- Writing algebraic expressions from words
- Evaluating expressions by substitution
- Combining like terms
- The distributive property
- One-step equations
- Two-step equations
- Inequalities on a number line
- Exponents and powers
- Percent change, tax, tip, and discount
What Is a Variable?
A variable is just a letter that stands in for an unknown number. Think of it like a mystery box — the letter x (or n, or any letter) holds a value we don't know yet.
Example: If x = 5, then x + 3 = 5 + 3 = 8.
Remember: Variable = Value hiding! The letter is just a placeholder for a number.
Reading Expressions
An expression is a math phrase made of numbers, variables, and operations like + or ×. It does NOT have an equals sign — it's just a phrase, not a full sentence.
Example: 3x + 7 means 'three times some number, plus seven.' If x = 2, that's 3×2 + 7 = 13.
Remember: No equals sign = expression. Equals sign = equation. Spot the difference!
Combining Like Terms
Like terms have the same variable — you can add or subtract them just like regular numbers. Terms with different variables (or no variable) must stay separate.
Example: 4x + 2x = 6x (same variable!), but 4x + 2 cannot be combined (different types).
Remember: Only combine terms that look alike — apples with apples, oranges with oranges!
Worked example
Simplify the expression: 2x + 4 + 3x + 1
- 1Step 1 — Find like terms: 2x and 3x are like terms. 4 and 1 are like terms.
- 2Step 2 — Combine the x terms: 2x + 3x = 5x.
- 3Step 3 — Combine the numbers: 4 + 1 = 5. Write them together: 5x + 5.
Answer: 5x + 5
The #1 mistake to avoid
Students often combine unlike terms — for example, writing 3x + 4 = 7x. Remember: x terms and plain numbers are different types and CANNOT be added together!
Key takeaways
- A variable is a letter that represents an unknown number.
- An expression is a math phrase with numbers and variables but NO equals sign.
- You can only combine like terms — terms that have the exact same variable.
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