Graphing & Writing Inequalities. What is an Inequality? Inequality – a comparison of two expressions > – greater than < – less than > – greater than or

Graphing & Writing

Inequalities

What is an Inequality?

Inequality – a comparison of two expressions

>– greater than

<– less than

>– greater than or equal to

<– less than or equal to

Equation vs. Inequality?

Equation – uses an equal sign; typically only one solution

Inequality – uses an inequality symbol;

infinite amount of solutions

Open Circle vs. Closed Dot

Hole (open circles) – are found when

there isn’t an “equal” involved in the sign

Dot (closed circles) – include that number that the dot in

on (is an “equal” involved in sign)

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Graphing Inequalities

Inequality GraphWord Sentence

x < 3 x is less than 3 0 1 2 3 4

x < 3 x is less than or equal to

3 0 1 2 3 4

Explanation: 3 is not included but all numbers less than 3 ARE included

Explanation: 3 IS included and all numbers less than 3 are also included


Inequality GraphWord Sentence

x > 3 x is greater than 3

0 1 2 3 4

x > 3 x is greater than or equal to

3 0 1 2 3 4

Explanation: 3 is not included but all numbers greater than 3 ARE included

Explanation: 3 IS included and all numbers greater than 3 are also included


Graph each inequality:

x > -2

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

4 > a

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



y < -3

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

t < 0

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



m > -4

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

t < 5

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

Writing InequalitiesInequalityWord

Sentence w > 6w is more than 6

x > 9x is at least 9

k < -7k is at most -7

g < 0g is less than 0

8 > j8 is greater than j

Adding & Subtracting Inequalities

We add and subtract inequalities just like equations – the inequality is like the equal sign

d - 7 < -2

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

+ 7 +7d < 5



9 + a > 11

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

-9 -9 a > 2



1 + s < 5

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

-1 -1 s < 4



2 > n - 1

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

+1 + 1 3 > n



3 + b < 1

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

-3 -3 b < -2

Solving Inequalities

Multiplying & Dividing

Multiplying & Dividing Inequalities

We multiply and divide inequalities just like equations – the inequality is like the equal sign

One MAJOR exception:

When multiplying or dividing by a negative number, the inequality flips


Why does the inequality flip?Example:

2 > -3

2 > -3 Multiply each side by a -1 for example

x -1 x -1-2 > 3 -2 is not greater than 3 so

we have to flip the sign

-2 < 3


Why does the inequality flip?Example:

8 > 6

8 > 6 Divide each side by a -2 for example

÷ -2 ÷ -2-4 > -3 -4 is not greater than -3

so we have to flip the sign

-4 < -3


Examples: m > -5

14Multiply each side by 14

m > -70

m > -514

(14) (14)


Examples: 15n > 450

Divide each side by 15

n > 30

15n > 45015 15


Examples: -3a < 12

Divide each side by -3 (notice we are dividing by a “negative” – sign will flip.

>

-3a < 12-3 -3

a -4


Examples: x < 1

-2Multiply each side by -2 – notice we are multiplying by a “negative” so the sign will flip

x < 1-2

(-2) (-2)

>x -2


Practice:

r < 3-6

r > -18

-15s > 30 s < -2

8h > 32 h > 4

x < 20 x < 10 2

Inequalities Problem Solving

A.) $9

B.) $13

C.) $15

D.) $16

Chico is saving for new shoes that cost $87. He already has $9 saved, and he will save the same amount each week. Chico wants to but the shoes in 6 weeks. Use the inequality below to determine the least amount Chico can save each week and still buy the shoes in 6 weeks.

9 + 6x ≥ 87

Documents

Graphing & Writing Inequalities. What is an Inequality? Inequality – a comparison of two expressions > – greater than < – less than > – greater than or