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Int. Alg. Notes
Section 3.4
Page 1 of 3
Section 3.4: Linear Inequalities in Two Variables
Big Idea: Sometimes you want to graph the situation where the outcome of a calculation involving two
variables is greater than or less than a given number. For those cases, we need to learn how to graph linear
inequalities in two variables to represent all the possible solutions.
Big Skill: You should be able to graph a linear equation in two variables.
Example of the type of problem we’ll learn to solve:
If you purchase p pair of pants at $29.95 each and s shirts at $18.99 each, how many of each can you buy and
not spend more than $120?
Support Skill: Determining if an ordered pair satisfies a linear inequality
 Plug in the numbers and see if you get a true inequality.
Practice:
1. Determine if (4, 1) is a solution of the linear inequality -2x + 3y  3.
2. Determine if (-1, 2) is a solution of the linear inequality -2x + 3y  3.
3. Determine if (0, 1) is a solution of the linear inequality -2x + 3y  3.
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Int. Alg. Notes
Section 3.4
Page 2 of 3
Main Skill: Graphing Linear Inequalities in Two Variables
 Step 1: Write the inequality as an equality, then graph the equation using a dashed line if it is a strict
inequality (< or >), or using a solid line if it is not a strict inequality ( or ).
 Step 2: Pick a test point and see if the test point satisfies the inequality.

If the test point satisfies the inequality, then shade the half of the plane containing the test point.

If the test point does not satisfy the inequality, then shade the other half.
Practice:
1. Graph the linear inequality y < -2x + 3.
2. Graph the linear inequality 6x – 3y  15.
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Int. Alg. Notes
Section 3.4
Page 3 of 3
3. If you purchase p pair of pants at $29.95 each and s shirts at $18.99 each, how many of each can you
buy and not spend more than $120? To solve, write the problem as an inequality, graph it, then read off
the ordered pairs.
4. If you are on a 1,500 calorie diet, and Wendy’s chicken breast filet has 430 calories, while a Frosty has
330 calories, how many of each can you eat and still maintain your diet?
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.