Elementary Algebra

An introduction to algebra: describing numerical relationships; the real numbers; exponents and order of operations; algebraic expressions; solving equations; problem solving; chapter review; chapter test. Real numbers, equations, and inequalities: adding and subtracting real numbers; multiplying, finding powers, and dividing real numbers; order of operations and evaluating algebraic expressions; simplifying algebraic expressions; solving equations; formulas; problem solving; inequalities; chapter review; chapter test; cumulative review exercises. Graphs, linear equations, and functions: graphing using the rectangular coordinate system; equations containing two variables; graphing linear equations using a graphing utility; rate of change and the slope of a line; writing equations of lines; functions; chapter review; chapter test. Solving systems of equations and inequalities: solving systems of equations by graphing; solving systems of equations by substitution; solving systems of equations by addition; applications of systems of equations; solving systems of linear inequalities; solving systems of three equations in three variables; chapter review; chapter test; cumulative review exercises. Exponents and polynomials: natural-number exponents; zero- and negative-integral exponents; scientific notation; polynomials; adding and subtracting polynomials; multiplying polynomials; dividing polynomials by monomials; dividing polynomials by polynomials; chapter review; chapter test; roots and radicals; square roots and the pythagorean theorem; nth roots and radicands that contain variables; solving equations containing radicals and the distance formula; simplifying radical expressions; adding and subtracting radical expressions; multiplying and dividing radical expressions; rational exponents; chapter review; chapter test; cumulative review. Quadratic equations: solving equations of the form x squared = c; completing the square; the quadratic formula; applications of quadratic equations; complex numbers; graphing quadratic functions; chapter review; chapter test. Rational expressions: the basic properties of fractions; multiplying fractions; dividing fractions; adding and subtracting fractions with like denominators; adding and subtracting fractions with unlike denominators; complex fractions; solving equations that contain fractions; ratio and proportion; chapter review; chapter test; cumulative review exercises.