Question

Solve the inequality. Show your work.
|r + 3| ≥ 7

Answer 1

Ok so this is greater that, do you know how to start?

Answer 2

No

Answer 3

well first, writeit two ways, greater than and less than

Answer 4

What does that mean?

Answer 5

ok well just to show you\[(r+3\ge7) or (r+3\le-7)\]

Answer 6

solve each of those

Answer 7

ok

Answer 8

4 or -4

Answer 9

close remember to subtract 3 from -7 is to add -3 to -7

Answer 10

10 or -10

Answer 11

4 or -10, you subtract 3 from both sides, do you understand or should I go back?

Answer 12

Please go back.

Answer 13

ok well first do you understand why you write it the two ways?

Answer 14

is it because its absolute value

Answer 15

right. |-5|=|5| they equal the same thing. so let's look at the first one the original. what does that look like now?

Answer 16

[|r+3|=|r+-3|

Answer 17

hold on slow down. let's look at that. I understand how you got there but let's look at it. if we plug in 5 for r, then |5+3|=|5-3| this gets us |8|=|2|. so try again. remember what the original problem is.

Answer 18

|r+3|=|r-3|

Answer 19

you're thinking about the wrong part. do you know what this will look like on a graph? kind of like that

Answer 20

what was inside the absolute value bars stays the same.

Answer 21

OK so it should look like this |r + 3|

Answer 22

ok let's think about it like this. we are trying to find what r is right?

Answer 23

yes

Answer 24

so we are told that the absolute value of r plus 3 is greater that or equal to 7.

Answer 25

Yes

Answer 26

so because r is inside the absolute value bars it can be negative or positive

Answer 27

Would R=4?

Answer 28

r will be 2 things because it is in the absolute value bars.
here to make it easier make the greater than or equal to an equal sign for now.
|r+3|=7
what do you do first.

Answer 29

Minus 3 from both sides
|r+3|=7
-3 -3
r=4

Answer 30

wait. slow down. let's just take 3 away for now.
|r|=7 what is r

Answer 31

-7

Answer 32

or...

Answer 33

4

Answer 34

ok if you have |r|=7 then r= 7 and r= -7
do you understand?

Answer 35

Yes, I understand

Answer 36

so if we write it out
|r|=7 and |r|=-7
so if we have |r+3|=7 how do we write it out

Answer 37

r ≤ -10 and r ≥ 4

Answer 38

just to make sure you understand so you can apply it later how do you get to that?

Answer 39

First I subtracted 3 from both sides
|r+3|=7
-3 -3
r=4

Answer 40

Then I added
-3+-7
And got
-10 which is greater than 7

Answer 41

-10 which is less than 7

Answer 42

ok let me show you the work I did
|r+3| ≥7
r+3 ≥7 r+3≤-7
r ≥4 r≤-10
plug both in to the original equation
|4+3| ≥7 |-10+3| ≥7
|7| ≥7 |-7| ≥7
7 ≥7 7 ≥7
does that make sence

Answer 43

Yes it does make sense. Thank you so much for everything, you have been a huge help to me.

Answer 44

No problem any time