Algebraic Expressions • Topic 1 of 7

Variables

A variable is a symbol, usually a letter such as x or n, that stands for an unknown or changing number. Variables let us write general rules and relationships: "a number increased by 5" becomes x + 5. The same variable always represents the same value within one problem, while different letters usually represent different quantities. Translating words into variable expressions is a core SAT skill — "twice a number" is 2x, "5 less than a number" is x − 5. Reading carefully for order matters: "5 less than x" is x − 5, not 5 − x.

✅ Solved examples

1. Write "a number increased by 7" as an expression.
Let the number be x; "increased by 7" means add 7, giving x + 7.
2. Write "twice a number" as an expression.
Twice means multiply by 2: 2x.
3. Write "5 less than a number n".
"5 less than n" subtracts 5 from n: n − 5.
4. If x represents Maria's age, write an expression for her age in 3 years.
Add 3 to her current age: x + 3.

✏️ Practice — try these, take hints as needed

1. Write "a number decreased by 4" as an expression.
Let the number be x.
Decreased means subtract.
x − 4.
x − 4.
2. Write "three times a number" as an expression.
Three times means × 3.
Use a variable x.
3x.
3x.
3. Write "8 more than twice a number x".
Twice x is 2x.
"8 more than" adds 8.
Combine.
2x + 8.
4. Write "the sum of a number and 10".
Sum means add.
Use x.
x + 10.
x + 10.
5. Write "7 less than a number x".
"Less than" subtracts.
Order: subtract 7 from x.
x − 7.
x − 7.

📝 Topic test — 8 questions

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