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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?.

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slide1

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
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
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
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
Let’s Try Some!

<

<

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

>

<

<

<

our friend the number line
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
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.

By shading in the

number line we are

indicating that all the

numbers in the shade

are also possible

answers.

you try this
You Try This…
  • Graph x < 10
you try this1
You Try This…
  • Graph x > -4
you try this2
You Try This…
  • Graph x > 200
you try this3
You Try This…
  • Graph 7 < x
let s go shopping
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
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
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 understand1
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 understand2
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 understand3
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
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
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
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
Solve Each Inequality & Graph

Example 1:

m + 14 < 4

-14 -14

m < -10

solve each inequality graph1
Solve Each Inequality & Graph

Example 2:

6y - 6 > 7y

-6y -6y

-6 > y

y < -6

solve each inequality graph2
Solve Each Inequality & Graph

Example 3:

k < 10

(-3)

(-3)

-3

k > -30