1.6 Intro to Solving Inequalities1.6 Intro to Solving Inequalities1.6 Intro to Solving Inequalities1.6 Intro to Solving InequalitiesHow is an inequality different from an equation?What transformations produce equivalent inequalities?When do you flip the inequality sign?What is a compound inequality?What is the difference between “and and “or”?

Properties of InequalityFor all real numbers a,b, and c, wherea b :

Addition Property

a c b c

Subtraction Property

a c b c

Multiplication Property

I f c 0, then ac bc I f c 0, then ac bc

Division Propertya b

I f c 0, thenc c

a bI f c 0, then

c c

Graphing Inequalities

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

Example 1Solve 8d 3 9. Graph the solution on a

8d 3 9

8d 12+3 +38 8

3d

2

number line.

-2 -1 0 1 2

Example 2Solve 2y 9 5y 15. Graph the solution

on a2y 9 5y 15

-2y -2y

number line.

-3 -2 -1 0 1

9 3y 15 -15 -156 3y

3 32 y

What happens to the inequality sign when you multiply or dividing an inequality by the same

negative number?

You reverse the inequality sign.

The weight w (in pounds) of an Icelandic saithe is given by

w = 10.4t −2.2Where t is the age of the fish in years.

Describe the ages of a group of Icelandic saithe that weigh up to 29 pounds.

3t

PracticeSolve each inequality, and graph the solution on a number line.

1) -x + 8 < 41 2) 4y – 12 > 7y - 15

Compound Inequalities

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

Example 3Solve 5x 7 3 and 3x 9 3. Graph

thesolution on a number line.

5x + 7 > –3 and 3x – 9 < 3

5x > –10 and 3x < 12

x > –2 and x < 4

Example 4Solve 3x 8 13 or 2x 1 3. Graph

thesolution on a number line.

3x – 8 13 or 2x + 1 –3

3x 21 or 2x –4

x 7 or x –2

PracticeGraph the solution of each compound inequality on a number line.

1) x + 9 < 5 and 4x >12

2) 20 – 3x > 11 or -4x < -20

How is an inequality different from an equation?What transformations produce equivalent inequalities?

When do you flip the inequality sign?What is a compound inequality?What is the difference between “and and “or”?

Assignment

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