INEQUALITIES

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# INEQUALITIES - PowerPoint PPT Presentation

INEQUALITIES. Targeted TEKS: A.10 The student understands there is more than one way to solve a Quadratic Equation and solves them using appropriate methods. (A) Solve Quadratic Equations using concrete models, tables, graphs, and algebraic methods. Equal or Unequal?.

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INEQUALITIES

Targeted TEKS:

A.10 The student understands there is more than one way to solve a Quadratic Equation and solves them using appropriate methods.

(A) Solve Quadratic Equations using concrete models, tables, graphs, and algebraic methods

Equal or Unequal?
• We call a math statement an EQUATION when both sides of the statement are equalto each other.
• Example: 10 = 5 + 3 + 2
• We call a math statement an INEQUALITY when both sides of the statement are not equal to each other.
• Example: 10 = 5 + 5 + 5
Inequality Signs
• We don’t use the = sign if both sides of the statement are not equal, we use other signs.

>

>

<

<

DON’T FORGET THIS!!!
• THE BIGGER SIDE OF THE SIGN IS ON THE SAME SIDE AS THE BIGGER #
• THE SMALLER SIDE OF THE SIGN IS ON THE SAME SIDE AS THE SMALLER #
• Examples: 10 15 or -4 -12

<

>

Let’s Try Some!

<

<

• 2 7
• -65 -62
• 32.3 32.5
• 3 5
• 22 10
• -10 4

>

<

<

<

Our Friend, The Number Line
• A number line is simply this…

…a line with numbers on it.

• We use a number line to count and to graphically show numbers.
• Example: Graph x = 5.
Graphing Inequalities
• Graph x = 2
• Graph x < 2
• Graph x < 2
• Graph x > 2
• Graph x > 2

A “closed” circle ( )

indicates we include

the number.

An “open” circle ( )

indicates we DO NOT

include the number.

number line we are

indicating that all the

are also possible

You Try This…
• Graph x < 10
You Try This…
• Graph x > -4
You Try This…
• Graph x > 200
You Try This…
• Graph 7 < x
Let’s Go Shopping!
• Last week you went shopping at the mall. You had \$150 to spend for the day. You bought a shirt for \$25 and some jeans for \$40. You also spent \$5 on lunch. You wanted to purchase a pair of shoes. What is the maximum amount of money you could have spent on the shoes?

\$150 >\$25 + \$40 + \$5 + x

The cost of

the shoes

The maximum amount you have

The amount you

have spent

How much can the shoes cost?

\$150 >\$25 + \$40 + \$5 + x

• Basically, the shoes must cost less than or equal to the amount you have left!

\$150 >\$70 + x

-\$ 70 -\$70

\$ 80 > x

The cost of

the shoes

Do You Really Understand?
• Let’s see if this makes sense…

(If we add 6 to both sides, is the inequality true?)

3 < 9

3+6 < 9+6

9 < 15

YES!

Do You Really Understand?
• Let’s see if this really makes sense…

(If we subtract 3 from both sides, is the inequality true?)

10 > 4

10-3 > 4-3

7 > 1

YES!

Do You Really Understand?
• Let’s see if this still really makes sense…

(If we multiply both sides by 2, is the inequality true?)

8 < 12

8(2) < 12(2)

16 < 24

YES!

Do You Really Understand?
• Let’s see if this still really makes sense…

(If we multiply both sides by -2, is the inequality true?)

8 < 12

8(-2) < 12(-2)

THIS STATEMENT

IS NOT TRUE. WE

NEED TO FLIP THE

INEQUALITY SIGN

TO MAKE THIS A

TRUE STATEMENT.

-16 < -24

-16 > -24

Solving Inequalities
• So apparently there are a few basic rules we have to follow when solving inequalities.
• If you break these rules you will answer the question incorrectly!
• DON’T BREAK THE RULZ!
Rule #1
• Don’t forget who the bigger number is!
• Example:

9 > x

• It is okay to rewrite this statement as

x < 9

• If 9 is bigger than “x”, that means that “x” is smaller than 9.
Rule #2
• When multiplying or dividing by a negative number, reverse the inequality sign.
• Example:

15 > -5x

-5 -5

-3 < x

Solve Each Inequality & Graph

Example 1:

m + 14 < 4

-14 -14

m < -10

Solve Each Inequality & Graph

Example 2:

6y - 6 > 7y

-6y -6y

-6 > y

y < -6

Solve Each Inequality & Graph

Example 3:

k < 10

(-3)

(-3)

-3

k > -30