1. 1.6 Intro to Solving Inequalities
Objectives:
Write, solve, and graph linear inequalities in one variable
Solve and graph compound linear inequalities in one variable

2. Properties of Inequality
For all real numbers a,b, and c, where
Addition Property
Subtraction Property
Multiplication Property
Division Property

3. Graphing Inequalities
To graph an inequality in one variable, use an open dot for < or > and a solid dot for < or >.

4. Example 1 Solve Graph the solution on a number line. +3 +3 -2 -1 1 2 8
+3 +3 -2 -1 1 2 8 8

5. Example 2 Solve Graph the solution on a number line. -2y -2y -15 -15 -3 -2 -1 1 3 3

6. What happens to the inequality sign when you multiply or dividing an inequality by the same negative number?
You reverse the inequality sign.

7. The weight w (in pounds) of an
Icelandic saithe is given by
w = 10.4t −2.2
Where t is the age of the fish in years. Describe the ages of a group of Icelandic saithe that weigh up to 29 pounds.

8. Practice
Solve each inequality, and graph the solution on a number line.
1) -x + 8 < 41
2) 4y – 12 > 7y - 15

9. Compound Inequalities
A compound inequality is two simple inequalities joined by “and” or “or”.

10. Example 3 Solve Graph the solution on a number line.
5x + 7 > –3 and 3x – 9 < 3
5x > –10 and 3x < 12
x > –2 and x < 4

11. Example 4 Solve Graph the solution on a number line.
3x – 8  or 2x + 1  –3
3x  21 or 2x  –4
x  7 or x  –2

12. Practice
Graph the solution of each compound inequality on a number line.
1) x + 9 < 5 and 4x >12
2) 20 – 3x > 11 or -4x < -20

13. Assignment
p.45, 13-24, 26-48, 49, 51