Sponge Page 98

Introduction to Inequalities

Page 99

What’s an inequality?

• Is a range of values,

rather than ONE set number

• An algebraic relation showing that a quantity is greater than or less than

another quantity.

: 75Example x

Symbols

Less than

Greater than

Less than OR EQUAL TO

Greater than OR EQUAL TO

Solutions….

You can have a range of answers……

-5 -4 -3 -2 -1 0 1 2 3 4 5

All real numbers less than 2

x< 2

Answers: 1, 0, -1, -2……….

Solutions continued…

-5 -4 -3 -2 -1 0 1 2 3 4 5

All real numbers greater than 2

x > 2

Answers in solution: 3, 4, 5, 6……..

Solutions continued….

-5 -4 -3 -2 -1 0 1 2 3 4 5

All real numbers less than or equal to 1

1x

Solutions continued…

-5 -4 -3 -2 -1 0 1 2 3 4 5

All real numbers greater than or equal to 0

0x

Did you notice….Some of the dots were solid and some were open?

-5 -4 -3 -2 -1 0 1 2 3 4 5

2x

-5 -4 -3 -2 -1 0 1 2 3 4 5

1x

If the symbol is or then the dot is solid, because it can be that given number as well.

If the symbol is > or < then dot is open because it can not be equal to that given number.

Key words for Inequalities

< >

Less than greater than

more than

≤ ≥Less than or equal to Greater than or equal to

Maximum minimum

No more than atleast

Example #1

Graph: y ≥ 4

-5 -4 -3 -2 -1 0 1 2 3 4 5

Remember when graphing your own inequality be sure to include the given number and a number higher and lower than the one given on number line!

Example 2

Graph: x ≤ 4

-5 -4 -3 -2 -1 0 1 2 3 4 5

Remember when graphing your own inequality be sure to include the given number and a number higher and lower than the one given on number line!

Example 3

Graph: y < -2

-5 -4 -3 -2 -1 0 1 2 3 4 5

Example 4

Graph x = 4

-5 -4 -3 -2 -1 0 1 2 3 4 5

Example 5

Graph x ≠ 2

-5 -4 -3 -2 -1 0 1 2 3 4 5

Example 6

-5 -4 -3 -2 -1 0 1 2 3 4 5

Write the inequality:

Example 7

Write the inequality:

-5 -4 -3 -2 -1 0 1 2 3 4 5

Write the inequality

1) More than 2,000 people attended the concert.

2) The minimum deposit for a new checking account is $75.

3) The number of club members is at least 25.

Tape notes on Page 99

YOUR TURN…..

1)Work on the front and back of notes extra practice problems

2)Check with me your answers and then you can get homework worksheet (YOU CAN START ON IT)

-Homework sheet will be taped on page 98