Chapter 1 The Basics

Water engineering calculations depend on reliable algebra. Flow, storage, concentration, pressure, and treatment problems all require careful work with numbers, expressions, equations, and inequalities. This chapter begins with real numbers and arithmetic, then develops sets, exponents, roots, polynomials, equations, lines, rational expressions, and inequalities. Units and physical restrictions remain part of every calculation. A solution is complete only when its algebra is correct, its units are appropriate, and its meaning is reasonable in context.

Learning outcomes.

By the end of this chapter, you should be able to:

• apply real-number, fraction, exponent, and root properties;
• represent sets and ranges using inequalities and interval notation;
• simplify, expand, factor, and divide algebraic expressions;
• apply the Remainder, Factor, and Rational Zeros Theorems;
• solve and check linear, quadratic, radical, and formula-based equations;
• determine equations of lines and interpret slope; and
• solve linear, polynomial, rational, and absolute-value inequalities.