Algebra & Equations

Variables and Expressions

A variable (like x or n) represents an unknown number. An expression is a combination of numbers, variables and operations — it has no equals sign.

Examples: 3x + 5   |   2(n − 4)   |   a² + b²

Simplifying Expressions

Collect like terms (same variable, same power).

Example: 5x + 3 − 2x + 7 = 3x + 10

Expand brackets: 3(2x + 4) = 6x + 12

Substitution

Replace the variable with a given value and evaluate.

Example: If x = 3 and y = −2, find 2x² − y
= 2(3)² − (−2) = 2 × 9 + 2 = 18 + 2 = 20

Solving Linear Equations

Perform the same operation on both sides to isolate the variable.

Example: 3x − 5 = 16
→ 3x = 21 → x = 7

Example: 2(x + 3) = 14
→ x + 3 = 7 → x = 4

Writing Equations from Word Problems

Translate the problem into algebra, solve, then interpret.

Example: “A number doubled plus 9 equals 25. What is the number?”
2n + 9 = 25 → 2n = 16 → n = 8

Inequalities

Solve like equations, but flip the inequality sign when multiplying/dividing by a negative.

Example: −2x > 8 → x < −4

Key Tips

• Always check your answer by substituting back in
• Write out each step — don't skip operations in your head
• For 'find the value of' questions, you are solving an equation