Equations and inequalities

An equation says that two expressions are equal. Solving it means finding every number that makes it true. Equations are how algebra answers real questions: how long, how much, how fast.

In this chapter, you will solve the main types of equations met in college algebra. You will also solve inequalities, whose answers are usually intervals.

This chapter covers the following topics:

Linear equations and applications

Solving linear equations, equations with fractions, equations with no solution or every solution, solving a formula for one variable, and word problems.

Quadratic equations

Solving quadratic equations by factoring, by square roots, by completing the square, and with the quadratic formula, the discriminant, and applications.

Complex numbers

The imaginary unit i, adding, subtracting, multiplying, and dividing complex numbers, and quadratic equations with complex solutions.

Other types of equations

Rational equations, radical equations, absolute value equations, equations of quadratic type, and higher-degree equations solved by factoring.

Inequalities

Linear and compound inequalities, absolute value inequalities, and polynomial and rational inequalities solved with a sign chart.

Practice questions

Practice problems on every section of this chapter, with full step-by-step solutions.

Before you start

This chapter uses the skills from Chapter 1, especially factoring, radicals, rational expressions, and interval notation.