Question

Solve the inequality. Graph the solution set.

2r – 9 – 6

Answer 1

\[2r-9 \ge - 6\]

Answer 2

Is it >, >=, <, or <=?

Answer 3

Alright. So we want to find r.
SO we want to get rid of -9.
How can we get rid of -9?

Answer 4

divide some numbers by 3

Answer 5

No. We want to get rid of -9, or cancel out.
How can we cancel out -9?

Answer 6

That was my only plan, I have no idea.

Answer 7

What's the opposite of subtraction?

Answer 8

addition

Answer 9

So how can we use addition to cancel out -9?
As in, what number add to -9 give us 0?

Answer 10

9

Answer 11

Good. -9 + 9 = 0
What's -6+9 ?

Answer 12

3

Answer 13

\[\large \large 2r \ge 3\] ^So we have that so far, correct? Does it make sense so far?

Answer 14

Yes

Answer 15

Alright. So how can we get r by itself?

Answer 16

add -2

Answer 17

Well. 2r is a coefficient. Which mean it is a number multiply by a variable.
So another way of writing 2r is 2 * r.
We want r by itself, so we want to get rid of 2.
To get rid of 2, we must use the opposite operation.
So what's the opposite of multiplication?

Answer 18

Division

Answer 19

So we do 2 divided by 2, which would give us 1.
Now, what's 2 divided by 3?

Answer 20

By the way, keep it as fraction form for now.

Answer 21

Also, I mean 3 divided by 2*

Answer 22

2/3

Answer 23

3 divided by 2* My bad.

Answer 24

3/2

Answer 25

Great. So now what does our inequality looks like?

Answer 26

3/2

Answer 27

r = 3/2

Answer 28

Where's our r? o_O
Did r vanish into thin air?

Answer 29

Well. It's not equal, since it's an inquality. It's r greater than or equal to 3/2.

Answer 30

You can leave it as 3/2 or you can put it into a mixed number or a decimal.

Answer 31

\[r \ge \frac{ 3 }{ 2 }\]

Answer 32

Yes. I prefer mixed number than improper fraction, since improper fraction is... improper.
You know what 3/2 in mixed number form?

Answer 33

\[1\frac{ 1 }{ 2 }\]

Answer 34

Great. So you can write it as r >= 1 1/2

Answer 35

ok

Answer 36

I hope this help! :)

Answer 37

Thanks