Topic A: Expressions
Writing, simplifying, and evaluating expressions.
01 — Writing & Evaluating
Writing & Evaluating Expressions
A variable (like x) is a box that holds a number we don't know yet.
- Writing: "5 more than a number" → x + 5. "twice a number" → 2x.
- Evaluating: plug the number in for the letter, then do the math.
- Like terms: only combine terms with the same letter. 3x + 2x = 5x, but 3x + 2 stays as is.
- Distributive property: 3(x + 4) = 3x + 12.
Example: If x = 4, then 2x + 7 = 2(4) + 7 = 15.
Practice — Writing & Evaluating Expressions
Q1 · Multiple Choice
Which expression means "6 less than three times a number"?
Q2 · Short Answer
Evaluate 4x − 5 when x = 3.
02 — Polynomials & Factoring
Multiplying & Factoring
The GED asks you to multiply simple polynomials and factor easy quadratics.
- FOIL: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6.
- Factoring x² + bx + c: find two numbers that multiply to c and add to b.
- Common factor: pull out what every term shares. 4x + 8 = 4(x + 2).
Example: x² + 7x + 10: 2 × 5 = 10 and 2 + 5 = 7, so it factors to (x + 2)(x + 5).
Practice — Multiplying & Factoring
Q3 · Multiple Choice
Which is (x + 4)(x − 1)?
Q4 · Multiple Choice
Factor: x² − 9x + 20
Topic B: Equations & Inequalities
Solving for x and word problems.
03 — Linear Equations
Solving Linear Equations
An equation is like a balance scale. Whatever you do to one side, do to the other side.
- Goal: get x alone on one side.
- Undo adding/subtracting first, then undo multiplying/dividing.
- Variables on both sides: move all the x's to one side first.
- Check: plug your answer back in to make sure it works.
Example: 3x + 5 = 20 → 3x = 15 → x = 5.
Practice — Solving Linear Equations
Q5 · Short Answer
Solve: 2x − 7 = 11
Q6 · Short Answer
Solve: 5x + 3 = 2x + 18
04 — Inequalities & Word Problems
Inequalities & Word Problems
Inequalities use <, >, ≤, ≥ instead of =. Solve them just like equations, with one special rule.
- Special rule: if you multiply or divide by a negative, flip the sign.
- Graphing: open circle for < or >, closed (filled) circle for ≤ or ≥.
- Word problems: name the unknown x, write an equation, solve, then answer the question asked.
- Key words: "at least" → ≥, "no more than" → ≤.
Example: −2x > 8 → divide by −2 and flip → x < −4.
Practice — Inequalities & Word Problems
Q7 · Multiple Choice
Solve: −3x ≤ 12
Q8 · Short Answer
A gym charges $25 to join plus $10 a month. Maria paid $85 total. How many months did she pay for?