8.18 Inequalities

Presentation

•

Mathematics

•

9th Grade

•

Hard

Rabah Issa

FREE Resource

17 Slides • 32 Questions

Things to Remember:

-The inequalities that contains the equal signs are closed circles when modeling on the number line.

-The inequalities without the equal sign are open circles when modeling on the number line.

Multiple Choice

Decide if the inequality is open circle or closed circle: 4x > 16

Open Circle

Closed Circle

Flip the sign

I don't know

Graphing Inequalities

When graphing your inequality on the number line, the open circle means the number is not included.
When graphing your inequality on the number line, the closed circle means the number is included.

VOCABULARY

What an inequality MEANS in an algebraic context.

Given: x - 3 = 7

If we solve it, x = 10

Which means we plug it in

10 - 3 = 7

7 = 7

7 = 7 is a true statement

So x is 10 and ONLY 10

Given: x - 3 > 7

If we solve it, x > 10

x has to be bigger than 10

So let's pick 15 and plug it in

15 - 3 > 7

12 > 7

12 > 7 is a true statement

So x is ANY NUMBER BIGGER THAN 10

Multiple Select

Given x > 3, choose all numbers that could be x.

-3

1,895

What an inequality MEANS continued

x = 5: "x equals 5" so x is 5

x < 5: "x is less than 5" so x is 4, 3, 2, 1 ,0, -1, -2 ...

x ≤ 5: "x is less than or equal to 5" so x is 5, 4, 3, 2, 1 ,0, -1, -2 ...

x > 5: "x is greater than 5" so x is 6, 7, 8, 9, 10, 11, 12 ...

x ≥ 5: "x is greater than or equal to 5" so x is 5, 6, 7, 8, 9, 10, 11, 12 ..

Multiple Select

Given x ≤ -7, choose all numbers that could be x.

-7

-9

-6

-1

-129

VOCABULARY

GRAPH: the collection of all points whose coordinates satisfy a given relation.

Example: x = 6

Example: x < 6

EXAMPLE: x ≥ -4

meaning all numbers bigger than four AND including four
so on the graph, we will use a CLOSED CIRCLE
Graphically is mean 6 is part fo the solution set or part of the answers

EXAMPLE: x > -4

Draw

Graph: x ≥ -1

Multiple Choice

Which graph represents

x < 3

Graphing Inequalities examples for reference

Multiple Choice

Which graph represents

x ≥ -17

What if the variable is on the right?

Circle rules are the same.

You may want to rewrite it but it has to 'eat' the same number or variable.

Example: 2 < x

Draw

Graph: -2 > x

Multiple Select

Which inequalities represent the graph?

x < -4

x > -4

-4 > x

-4 < x

Multiple Choice

Which situation can be represented by the inequality

$h\ \ge\ 45$ ?

You must do more than 45 minutes of homework tonight

I've been watching TV for 45 minutes.

You can eat no more than 45 M&M's

You must be at least 45 inches tall to ride the rollercoaster.

Review...

Multiple Choice

How would you graph the following inequality:

$c\ \le\ -4$

open circle on -4, arrow to the right

open circle on -4, arrow to the left

closed circle on -4, arrow to the right

closed circle on -4, arrow to the left

Multiple Choice

CJ had $500 in his account at the beginning of the summer. He wants to have at least $200 left in his account by the end of summer. He withdraws $25 each week for food, clothes, and games. Which inequality represents CJ's situation?

$500\ +\ 25x\ \le\ 200$

$500\ -\ 25x\ \ge\ 200$

$500\ -\ 25x\ \le\ 200$

$500\ +\ 25x\ >\ 200$

Multiple Choice

Greater than or equal to

≤

≥

Multiple Choice

Greater than

≤

≥

Multiple Choice

Less than or equal to

≤

≥

Multiple Choice

When graphing an inequality, you use an OPEN dot when you use which symbol?

<, >

≤, ≥

≤, <

≥, >

Multiple Choice

When you graph an inequality, you used a CLOSED dot when you use which symbols?

≤, ≥

<, >

≤, <

≥, >

Multiple Choice

Match the graph with its inequality.

a < 11

a > 11

a ≥ 11

a ≤ 11

Multiple Choice

Which inequality is represented by the following graph

x < -8

x > -8

x ≥ -8

x ≤ -8

Multiple Choice

When graphing an inequality on the number line the OPEN circle means the number is______?

Not included

Included

Try to solve this on paper!

What would you do first?

What would you do second?

WHAT MUST YOU DO?

Multiple Choice

You flip an inequality symbol when you...

subtract

multiply and divide only

multiple by a negative number

multiple or divide by a negative number

Multiple Choice

Solve and choose the correct graph:

Multiple Choice

-4x + 14 ≤ 54

x ≥ - 10

x ≤ -10

x ≥ 10

x ≤ 10

Multiple Choice

What is this symbol?

less than

greater than

less than or equal to

greater than or equal to

Example 1

- 8x + 2x - 16 < - 5x + 7x

(-8x + 2x) - 16 < (-5x + 7x)

-6x - 16 < 2x

-6x - 16 - 2x < 2x - 2x

-8x - 16 < 0

-8x - 16 + 16 < 0 + 16

-8x < 16

-8x/-8 < 16/-8

x > -2

Multiple Choice

$Solve:\ -7\left(n-6\right)<91$

$n<7$

$n>7$

$n<-7$

$n>-7$

Multiple Choice

$\frac{3}{4}x+5>11$

$x>8$

$x>-8$

$x>-1$

$x<4$

Multiple Choice

Do I need to flip my sign?
-3x ≥ 12

Yes

Multiple Choice

-2x + 3(-4x + 6) ≤116

x ≤ -7

x ≥ 29

x ≥ -7

x ≤ 29

Multiple Choice

$−5(2𝑥+2)+5x>15$

$x<-5$

$x<5$

$x>5$

$x>-5$

Multiple Choice

3x - 5 > -26

x < -7

x > -7

x > 7

x < 7

Multiple Choice

6(n + 2) < -72

n < -14

n < 35/3

n < -10

n > -14

Multiple Choice

4(2a + 3) < 3(a - 1)

a < -3

a > -3

a < 3

a > 3

Multiple Choice

Solve:
6x+10>5x-12

x>2

x<2

x<-22

x>-22

Things to Remember:

-The inequalities that contains the equal signs are closed circles when modeling on the number line.

-The inequalities without the equal sign are open circles when modeling on the number line.

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