Vocabulary
A term is separated by addition or subtraction. A coefficient multiplies a variable, and a constant has no variable.
ExampleIn 4x² − 3x + 7, the terms are 4x², −3x, and 7.
Chapter 01 of 10
Expressions
How do letters and numbers work together in algebra?
An expression represents a quantity. It can contain numbers, variables, and operations, but it does not make a claim with an equals sign. Learning to read expressions accurately is the foundation for every later chapter.
The big ideas
Understand these before you worry about speed.
Evaluate by substituting
Replace each variable with its given value, use parentheses, and then follow the order of operations.
ExampleIf x = −2, then 3x + 5 = 3(−2) + 5 = −1.
Combine like terms
Terms combine only when their variable parts match exactly. Add or subtract their coefficients; keep the variable part.
Example5x + 2 − 3x + 7 = 2x + 9.
Worked example
Follow the reason for each step—not just the symbols.
Problem
Simplify 3(2x − 5) + 4x + 9.
- Distribute 3: 6x − 15 + 4x + 9.
- Combine variable terms: 6x + 4x = 10x.
- Combine constants: −15 + 9 = −6.
Answer10x − 6
Try it yourself
Work on paper first. Open each answer only when you are ready to check.
1
Evaluate 2a² − 3 when a = −2.
Check answer
52
Simplify 7x + 4 − 2x + 9.
Check answer
5x + 133
Simplify −2(3y − 4) + y.
Check answer
−5y + 84
Write an expression for five less than twice n.
Check answer
2n − 5Practice and tools
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