Algebra
What to know
Expect items on simplifying expressions, solving linear equations and inequalities, slope and intercepts, systems of equations, exponent rules, polynomial operations and factoring, quadratic equations, function notation, and pattern/sequence reasoning. You should be able to translate a verbal relationship into an equation, solve it, and interpret the solution in context.
Traps
- Distributing a negative: −2(x − 5) = −2x + 10, not −2x − 10.
- Multiplying or dividing an inequality by a negative reverses the inequality symbol.
- Slope is rise over run; keep the sign consistent when subtracting coordinates.
- Function notation f(2) means “the output when the input is 2,” not f times 2.
- Dividing both sides by a variable can discard a valid solution; factor instead when a variable appears in every term.
- Always substitute back to catch sign errors and extraneous solutions.
Worked example
Solve 3(x − 2) = 5x + 8. Distribute: 3x − 6 = 5x + 8. Subtract 3x: −6 = 2x + 8. Subtract 8: −14 = 2x. Divide by 2: x = −7. Check: left side 3(−9) = −27; right side 5(−7) + 8 = −27. Both sides match, so the solution is confirmed. Rule of thumb: simplify each side separately, collect variables on one side, then check by substitution-checking takes seconds and catches most careless errors.