Basic Algebra in 98 Flashcards: Linear Equations, Inequalities and 46 Worked Examples
Learn basic algebra with deck YL5272: 46 worked solutions for linear equations and inequalities, plus the systems and interval notation you must add yourself.
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Most algebra decks are glossaries. YL5272 — Basic Algebra: Linear Equations & Inequalities (98 cards, free on Flip It) is the opposite: 46 of its cards are worked problems with the full solution written step by step on the back. That builds real solving speed — once you notice that many of its questions lost their instruction word.
Study this deck: Basic Algebra: Linear Equations & Inequalities
1 / 10Algebra
Tap the card for the answer · swipe right if you knew it, left if not
The stripped-verb problem
Seventeen fronts begin mid-sentence: for x: x + 7 = 15, for y: -2y = 14, for w in A = lw. The word Solve was cut. Twelve other cards kept it (Solve: 3x - 5 = 2x + 7), so one task appears in two shapes, and cards 48–49 (3x + 5 when x = 2) lost their Evaluate. The mathematics is fine — just read every front starting with "for" as "Solve for".
Ten cards from the deck
| Front | Back |
|---|---|
| Fundamental principle of equation solving | Whatever operation is applied to one side must also be applied to the other to maintain balance |
| for x: 2x - 6 = 10 | x = 8. Add 6 to both sides: 2x = 16, then divide by 2: x = 8 |
| Solve: 4(x - 3) = 2(x + 6) | x = 12. Distribute: 4x - 12 = 2x + 12, subtract 2x: 2x - 12 = 12, add 12: 2x = 24, divide by 2: x = 12 |
| Solve a linear inequality | Same operations as equations, but when multiplying or dividing by a negative number, reverse the inequality sign |
| Solve: -3x > 12 | x < -4. Divide both sides by -3 and reverse the sign |
| Solve: 2x + 3 = 2x + 5 | No solution. Subtracting 2x gives 3 = 5, which is false (inconsistent equation) |
| Solve: 3(x + 1) = 3x + 3 | All real numbers (identity). Distributing gives 3x + 3 = 3x + 3, always true |
| Zero product property | If ab = 0, then either a = 0 or b = 0 (or both) |
| Find the GCF of 12x and 18x² | 6x (largest factor common to both terms) |
| for h in A = (1/2)bh | h = 2A/b. Multiply both sides by 2, then divide by b |
What the 98 cards cover
Variable, constant, coefficient, term, like terms, algebraic expression; identity versus conditional equation; commutative, associative and distributive properties; the addition and multiplication properties of equality; additive and multiplicative inverses; isolating a variable, substitution, opposite operations; inequality signs ≤ and ≥ and the sign-reversal rule; monomial, binomial, trinomial, degree of a polynomial; x⁰ and x¹; the zero product property; GCF factoring; inconsistent equations and identities; literal equations and formula rearrangement (A = lw, A = ½bh, d = rt).
Two gaps to fill before an exam
The deck never solves a system. Card 34 defines a system of linear equations and card 35 says the solution is the intersection point of the graphs — then nothing. No substitution, no elimination, not one worked example, despite the title. Write six cards yourself: two by substitution, two by elimination, one with no solution (parallel lines), one with infinitely many.
Inequality answers stop halfway. Every inequality card ends at a bare x > 4. No interval notation, no number line, no compound or absolute-value inequalities. Add the two notations to each answer — (4, ∞) and the shaded ray — because that is the form most exam papers demand.
The deck's order is also not progressive: card 41 (2(x + 4) = 3x - 1) comes long before card 53 (2x + 3x), and five separate cards drill combining like terms. Sort by type on the first pass, then shuffle.
Search deck code YL5272 in the Flip It library to start.
Next in algebra: Master Quadratic Equations and Linear Systems · From Exponent Rules to Eigenvalues
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