Question

Please solve each of the inequalities below and graph the solution on a number line. It will be beneficial to you to show work on all problems so your instructor may provide specific feedback. However, to receive full credit for this assignment, you must show work for #4 and 5. You may either use a paint program, power point, or any program you choose to create the number line graphs, draw the graphs by hand and scan, or describe the graph in words. For example, x > 3 would be “x is greater than 3. The graph would have an open circle on 3 with shading to the right.”

Answer 1

#1-5 (1 point each)

1. x – 3 > –9

2. –2x + 1 ≤ –11

3. 10 < –3x + 1

4. 2(x + 5) > 8x – 8

5. –2(x – 3) ≥ 5 – (x + 3)

Answer 2

@jim_thompson5910 PLEASE HELP ME!! I BEGG :)

Answer 3

Let's do these one at a time

Answer 4

1.

x – 3 > –9

Answer 5

How do we solve that?

Answer 6

MMMMMMMM We have to figure out what X is

Answer 7

How do you do that? lol

Answer 8

you want to isolate x

Answer 9

or get x all by itself

Answer 10

how do we move that -3 over?

Answer 11

mmmm by doing it to both sides??

Answer 12

What can we add/subtract to both sides to get rid of that -3?

Answer 13

x? :/

Answer 14

-3 + what = 0

Answer 15

3

Answer 16

good, so add 3 to both sides, what do you get?

Answer 17

x > -6

Answer 18

perfect

Answer 19

so how do we graph this? any ideas?

Answer 20

Can you tell me step by step without words how we did that so i put it on my paper

Answer 21

x - 3 > -9

x - 3+3 > -9+3

x > -6

Answer 22

That sums up what we did

Answer 23

alright :)

Answer 24

how do we graph x > -6 ?

Answer 25

mmmmmmm idk

Answer 26

To graph the inequality x > -6, draw out a number line.


Then plot an open circle at -6.


Then shade to the right of the open circle.

Answer 27

Im going to put that ^^^ it says that i can do it in words so :)

Answer 28

yeah i prefer that over trying to draw (i suck at drawing lol)

Answer 29

LMAO me too :)

Answer 30

now.... number 2

Answer 31

–2x + 1 ≤ –11

Answer 32

What's the first step?

Answer 33

mmmmm its a guess.....i know its wrong but i think you have to subtract 1 from each side

Answer 34

it's a good guess because it's correct

Answer 35

ohh lol yaaay

Answer 36

–2x + 1 ≤ –11

–2x + 1-1 ≤ –11-1

–2x ≤ –12

Answer 37

what's next?

Answer 38

divide both sides by -2 ?

Answer 39

good, this will flip the sign

Answer 40

–2x + 1 ≤ –11

–2x + 1-1 ≤ –11-1

–2x ≤ –12

x ≥ –12/(-2)

x ≥ 6

Answer 41

alright :)

Answer 42

next graphing this

Answer 43

ok...

Answer 44

how do we do that?

Answer 45

draw a number line

Answer 46

good, what's next?

Answer 47

plot a closed circle at 6

Answer 48

good, then what?

Answer 49

shade to the...........right?

Answer 50

perfect

Answer 51

ok hold on let me write that

Answer 52

ok

Answer 53

ok number 3

Answer 54

10 < –3x + 1

Answer 55

first step?

Answer 56

mmmmmm subtract 1 from both sides?!

Answer 57

good, giving you what?

Answer 58

9 < -3x

Answer 59

then what's next?

Answer 60

divide both sides by -3

Answer 61

good, keep in mind the sign will flip

Answer 62

so doing that gives you what?

Answer 63

3 < x

Answer 64

close

Answer 65

9 < –3x


9/(-3) > –3x/(-3)


-3 > x

and that flips to this

x < -3

Answer 66

so the full steps are

Answer 67

10 < –3x + 1


10 -1 < –3x + 1 -1


9 < –3x


9/(-3) > –3x/(-3)


-3 > x


x < -3

Answer 68

To graph the inequality, draw out a number line.
Then plot an open circle on -3
Then shade to the right of the open circle.

Answer 69

close, it's to the left

Answer 70

everything else is perfect though

Answer 71

ohh ok :)

Answer 72

< means shade to the left

> means shade to the right

Answer 73

alright.... number 4

Answer 74

2(x + 5) > 8x – 8

Answer 75

First step is to distribute

Answer 76

2(x + 5) > 8x – 8

2x + 10 > 8x – 8

Answer 77

what's next?

Answer 78

subtract 10 from both sides?

Answer 79

good

Answer 80

what does that give you?

Answer 81

2x > 8x - 18

Answer 82

then what?

Answer 83

divide both sides by 2??

Answer 84

not yet, you subtract 8x from both sides

Answer 85

Add 18 to both sides?

Answer 86

no, subtract 8x from both sides

Answer 87

you want to get all the x terms to the left side

Answer 88

-6x - 18 ??

Answer 89

oh wait

Answer 90

idk

Answer 91

you forgot the inequality sign

Answer 92

-6x > -18

Answer 93

then what?

Answer 94

divide both sides by -6

Answer 95

giving you ???

Answer 96

x > 3

Answer 97

close

Answer 98

the sign will flip because you're dividing both sides by a negative number