- Ch. 1Look at a and 1A letter is a slot: always true means identity; true for a few means equation.
- Ch. 2Linear Equations in One UnknownAn equation is a level balance. Do the same to both sides until x is revealed.
- Ch. 3Linear Equations with Letter CoefficientsAt ax = b, do not divide yet: a ≠ 0; a = 0, b ≠ 0; both 0. Three endings.
- Ch. 4Using and Rearranging Linear EquationsAbsolute values, repeating decimals: split into pieces or × 10, and get ax = b.
- Ch. 5Linear Systems in Two UnknownsEquations are lines. Elimination draws a vertical line through their crossing.
- Ch. 6Linear Systems in Several UnknownsThree unknowns: eliminate one, then another, then walk back down the staircase.
- Ch. 7Learning to Complete the SquareFill the corner of x²+bx to get a square; squares are never negative.
- Ch. 8Solving Quadratic EquationsSquare roots, completing the square, formula, factoring. Pick the easiest road.
- Ch. 9The DiscriminantWithout solving, Δ = b² − 4ac tells you: two real roots, one, or none.
- Ch. 10Vieta's FormulasThe sum and product of the roots sit in the coefficients. Check Δ first.
- Ch. 11Higher-Degree EquationsSwap a repeated block for t, or factor, to reduce it to a quadratic.
- Ch. 12Fractional EquationsMultiply by the common denominator, then check every root, since it may be 0.
- Ch. 13Radical EquationsSquaring removes the root but lets in ghost-branch roots, so always check.
- Ch. 14Quadratic Systems in Two UnknownsSolutions are common points. Substitute a linear equation, or use Vieta.
- Ch. 15Integer Solutions of EquationsInteger solutions are lattice points: divide, factor, bound, check parity.
- Ch. 16Integer Roots of Quadratic EquationsFor integer roots Δ must be a perfect square; Vieta and factoring do the rest.
- Ch. 17Word Problems with EquationsDraw the story as a distance–time graph. Where the lines cross is the solution.
- Ch. 18A Map of EquationsThe whole volume in one picture: every equation reduces to ax = b.