Solving Multi-Step Linear Inequalities in Two Variables

Compare the inequalities given below. Notice that the first inequality includes one variable. The second inequality, however, includes two variables.

Inequality 1
3x − 6 > 18

Inequality 2
3x − 6y > 18

You are familiar with the process needed to solve the first inequality:

3x − 6   >   18

    + 6     + 6
_________________

3x     >     24
____         ____

3               3

x     >     8

When you consider the second inequality, how would you solve that one? How do you solve an inequality that includes two variables?

3x − 6y   >   18

?

During this topic, you will learn the process to solve an inequality that includes two variables, as well as how to represent the solutions both algebraically and graphically.