Inequalities

In

Algebra County

Types of inequalitysymbols

How to read inequalities

5xx is greater than 5

5x

x is greater than

or equal to 5

5x

x is less than 5

5x

x is less than or equal to 5

4 is less than x

4 x

x 4x is greater than 4

Examples

“Mike, you cannot eat more than 3 hot dogs.”

Let h = hot dogs

3h

“I can onlyspend $90

on groceriestoday.”

Let d = dollars spent

90d

“There are more than 200 people here today.”

Let p = number of people

200p

“Every adult could have32 teeth.”

Let t = number of teeth

32t

“I have lessthan 50

pennies inmy bank.”

Let p = number of pennies

50p

“The nationaldebt is morethan three

million dollars.”

Let d=dollars in debt

$3,000,000d

Graphing them on a line graph

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

3h

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

3h

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

3h

h is everthing except “3.”

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

3h

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

3h

Can we use the same methods for solving inequalities as we used for solving equations?

2 3 11x

Yes, except for when we multiply

or divide by a negative number.

What do we do when we multiply

or divide by a negative number?

Switch the inequality sign.

Solvinginequalities:

examplesCopy on your notes

3 5 2x-5 -5

3 3xThat’s legal.

3 3That’s legal too. 1x

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

1x -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Then we write this in set builder notation:

1x x

4 1 11x+1

+1 4 12x

-4

-4 3x

That’s legal.

That’s only legal if you switch the inequality sign.

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

3x x

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

In set builder notation:

3x

4 3

64x 4

3 24x 3 3

That’s only legal if you switch the inequality sign.

8x

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2

8x

In set builder notation:

8x x

TheEnd