linear

1. Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 3.1 - 1
Linear Inequalities
in One Variable

2. Solving inequalities is closely related to solving
equations. Inequalities are algebraic
expressions related by
We solve an inequality by finding all real
number solutions for it.

3. Linear Inequality
An inequality says that two expressions are not equal.
Linear Inequality
Examples:

4. Solving Linear Inequalities
Using the Addition Property
• Solving an inequality means to find all the
numbers that make the inequality true.
• Usually an inequality has infinite number of
solutions.
• Solutions are found by producing a series of
simpler equivalent equations, each having the
same solution set.
• We use the properties of inequality to produce
equivalent inequalities.

5. Solve and graph the solution:
Check: Substitute –4 for x in the equation x – 5 = 9.
The result should be a true statement.

6. Solve and graph the solution:
Now we have to test a number on each side of –4 to
verify that numbers greater than –4 make the inequality
true. We choose –3 and –5.
Using the Addition Property
of Inequality
–5 –4 –3 –2 –1 0 1 2 3 4 5

7. 3.1 Linear Inequalities in One Variable
Using the Addition Property of Inequality
Solve and graph the solution:
Check: Substitute 3 for m in the equation 3 + 7m = 8m.
The result should be a true statement.

8. Multiplication Property of Inequality
Multiplication Property of Inequality

9. Using the Multiplication Property
of Inequality
Solve and graph the solution:
Check: Substitute –8 for m in the equation 3m = –24.
The result should be a true statement.

10. 3.1 Linear Inequalities in One Variable
Using the Multiplication Property of Inequality
Solve and graph the solution:
Now we have to test a number on each side of –8 to
verify that numbers greater than or equal to –8 make the
inequality true. We choose –9 and –7.
–16 –14 –12 –10 –8 –6 –4 – 2 0 2 4

11. 3.1 Linear Inequalities in One Variable
Using the Multiplication Property of Inequality
Solve and graph the solution:
Check: Substitute – 5 for k in the equation –7k = 35.
The result should be a true statement.
This shows –5
is a boundary
point.

12. 3.1 Linear Inequalities in One Variable
Using the Multiplication Property of Inequality
Solve and graph the solution:
Now we have to test a number on each side of –5 to
verify that numbers less than or equal to –5 make the
inequality true. We choose –6 and –4.
–16 –14 –12 –10 –8 –6 –4 – 2 0 2 4