Topic A: Expressions & Properties
Lessons 1–4 · Simplifying, distributing, and writing algebraic expressions.
01–02 — Lessons 1–2
Writing & Simplifying Expressions
- Variable: a letter representing an unknown quantity.
- Term: a number, variable, or product (e.g., 3x, −5, 7xy).
- Like terms: same variable and same exponent — can be combined.
- Distributive property: a(b + c) = ab + ac.
- Combining: 4x + 2 + 3x − 7 = 7x − 5
2(3x − 4) + 5x = 6x − 8 + 5x = 11x − 8
Practice — Lessons 1–2
Q1 · Short Answer
Simplify: 5(2x + 3) − 4x. Give the coefficient of x.
Q2 · Multiple Choice
Which are like terms?
03–04 — Lessons 3–4
Writing Equations from Context
- Translate words to math: 'more than' = add, 'less than' = subtract, 'times' = multiply.
- 'Is' or 'equals' = the = sign.
- Define your variable clearly before writing the equation.
- Check your equation makes sense in context.
'A number increased by 7 is 15' → n + 7 = 15 → n = 8.
Practice — Lessons 3–4
Q3 · Short Answer
'Three times a number decreased by 4 equals 11.' Solve for the number.
Q4 · Multiple Choice
Which equation represents: 'twice a number plus 5 equals 17'?
Topic B: Solving Equations & Inequalities
Lessons 5–10 · Multi-step equations, literal equations, and inequalities.
05–07 — Lessons 5–7
Multi-Step Equations
- Use inverse operations to isolate the variable.
- Order of operations in reverse: first undo addition/subtraction, then multiplication/division.
- Variables on both sides: move all variable terms to one side.
- Distribute first when there are parentheses.
- Check: substitute your answer back into the original equation.
3(x − 2) = 2x + 5 → 3x − 6 = 2x + 5 → x = 11. Check: 3(9) = 27 = 22+5 ✓
Practice — Lessons 5–7
Q5 · Short Answer
Solve: 4x − 3 = 2x + 9.
Q6 · Multiple Choice
What is the first step to solve 2(x + 4) = 18?
08–10 — Lessons 8–10
Inequalities & Compound Inequalities
- Solving: same as equations, BUT flip the inequality when multiplying/dividing by a negative.
- Graph on a number line: open circle for < or >; closed circle for ≤ or ≥.
- And (compound): both conditions must be true — solution is the overlap.
- Or (compound): at least one condition is true — union of both solutions.
−2x + 3 > 7 → −2x > 4 → x < −2 (flip because dividing by −2)
Practice — Lessons 8–10
Q7 · Multiple Choice
When solving −3x > 9, what happens to the inequality sign?
Q8 · Short Answer
Solve: 5x + 2 ≤ 17.