Algebra and Trigonometry, 5th Edition

1.5 Linear Equations, Functions, Zeros, and Applications

• Solve linear equations.

• Solve applied problems using linear models.

• Find zeros of linear functions.

An equation is a statement that two expressions are equal. To solve an equation in one variable is to find all the values of the variable that make the equation true. Each of these values is a solution of the equation. The set of all solutions of an equation is its solution set. Some examples of equations in one variable are

$$\begin{array}{l}2x+3=5,3(x-1)=4x+5,\\ x^2-3x+2=0,\text{and}\frac{x-3}{x+4}=1.\end{array}$$

Linear Equations

The first two equations above are linear equations in one variable. We define such equations as follows.

A linear equation in one variable is an equation that can be expressed in the form $mx+b=0$, where ...