Algebra: Key Terms, Expressions and Linear Equations
Algebra uses letters to represent unknown or changing values and rules to manipulate them.
Key terms
A variable is a letter representing a value; a coefficient multiplies a variable; a constant has no variable; a term is a part separated by + or −; and an expression combines terms without an equals sign. Like terms have the same variable part.
Substitution and simplification
- For x = 4, 3x + 2 = 3(4) + 2 = 14.
- 2a + 5a − 3 = 7a − 3 because like terms combine.
- Expand 3(x + 2) = 3x + 6.
Linear equations
Keep an equation balanced by performing the same operation on both sides. Reverse addition with subtraction, multiplication with division, and so on.
Worked examples and practice
- 2x + 5 = 17 gives 2x = 12 and x = 6.
- Solve 3(y − 2) = 15: y − 2 = 5, so y = 7.
- Simplify 4a + 3 − 2a + 5 and solve 5x − 4 = 21.
