Algebra Foundations: Unit Review
Key rules and problem types from signed numbers through proportions and percents.
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Study Smart Tips for Algebra Foundations: Unit Review
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Questions Covered in This Set
12 cards to master
Why does 8 − 3 + 2 equal 7, not 3?
Addition and subtraction are done left to right: (8 − 3) + 2 = 5 + 2 = 7.
What is the difference between −3² and (−3)²?
−3² = −9 (exponent applies only to 3); (−3)² = 9 (the negative is inside the parentheses).
Rule for multiplying/dividing signed numbers
Same signs → positive result; different signs → negative result.
How do you subtract a negative, e.g. 5 − (−2)?
Add the opposite: 5 + 2 = 7.
Simplify vs. solve
You simplify an expression (3x + 5x − 2 = 8x − 2); you solve an equation for a value (8x − 2 = 14 → x = 2).
Distribute: −4(x − 3)
−4x + 12 — multiply every term inside, keeping track of signs.
Order of steps to solve 2x + 7 = 19
Undo in reverse: subtract 7 (2x = 12), then divide by 2 (x = 6). Check: 2(6)+7 = 19 ✓
The one extra rule for inequalities
Flip the inequality sign when you multiply or divide both sides by a negative: −2x < 10 → x > −5.
How do you solve a proportion like 3/4 = x/20?
Cross-multiply: 4x = 60, so x = 15.
Percent change formula
(new − old)/old × 100. Example: 250 → 310 gives 60/250 = 24% increase.
What happens when variables cancel in an equation?
False statement (−6 = 5) → no solution; true statement (5 = 5) → infinitely many solutions.
Basic percent relationship
part = percent × whole. A $80 jacket at 35% off: 0.65 × 80 = $52.
