Understanding Elementary Algebra with Geometry

The integers: what is algebra? introduction and basic notation; integers; adding integers; subtracting integers; multiplying and dividing integers; the real number system; chapter summary; review exercises, and practice test. Algebraic expressions: variables and exponents; algebraic substitution; the distributive property and combining like terms; simplifying algebraic expressions; translating phrases and sentences algebraically; chapter summary; review exercises, and practice test. First-degree equations and inequalities: types of equations and basic properties of equalities; solving first-degree equations in one variable and applications; more first-degree equations and applications; types of inequalities and basic properties of inequalities; solving first-degree inequalities in one variable and applications; chapter summary, review exercises, and practice test; cumulative review and practice test - chapters 1-3. Rational expressions: fundamental principle of fractions; multiplying and dividing rational expressions; adding and subtracting rational expressions; solving fractional equations and inequalities; ratio and proportion; verbal problems; chapter summary, review exercises, and practice test. Graphing straight lines: the rectangular (Cartesian) coordinate system; graphing a linear equation in two variables; the slope; the equation of a line. Interpreting graphs and systems of linear equations: interpreting graphs; solving systems of linear equations - graphical method; solving systems of linear equations - algebraic methods; verbal problems; chapter summary, review exercises, and practice test; cumulative review and practice test - chapters 4-6. Exponents and polynomials: exponent rules; zero and negative exponents; scientific notation; introduction to polynomials; multiplying polynomials; special products; chapter summary, review exercises, and practice test. Factoring: common factors; factoring trinomials; more factoring; solving polynomial equations by factoring; dividing polynomials; chapter summary, review exercises, and practice test. More rational expressions: reducing rational expressions; multiplying and dividing rational expressions; adding and subtracting rational expressions; fractional equations; literal equations; verbal problems; chapter summary, review exercises, and practice test; cumulative review and practice test - chapters. Radical expressions and equations: definitions and basic notation; properties of radicals and simplest radical form; adding and subtracting radical expressions; multiplying and dividing radical expressions; radical equations; chapter summary, review exercises, and practice test. Quadratic equations: the factoring and square root methods; the method of completing the square; the quadratic formula; choosing a method; verbal problems; graphing quadratic equations; chapter summary, review exercises, and practice test.