Question

whats 3|3k|=27 ?

Answer 1

First we must divide both sides by 3


3|3k| = 27


|3k| = 27/3


|3k| = 9

Answer 2

Then we use the idea that if |x| = p, then x = p or x = -p to go from this equation

|3k| = 9

to these two equations

3k = 9 or 3k = -9

Answer 3

solve those last two equations to get your two answers

Answer 4

9

Answer 5

3k = 9, so k = ??

Answer 6

3k means "3 times k"

Answer 7

\(3|3k| = 27\)

Divide by 3

\(|3k| = 9\)

Figure out that 3 is positive and the absolute values do nothing

\(3|k| = 9\)

Divide by 3

\(|k| = 3\)

Easier yet?

Answer 8

how do you get 27

Answer 9

?? From the problem statement?

Answer 10

Do you mean to say some answer key says a solution is k = 27? That would be incorrect.

Answer 11

yea.

Answer 12

AS WRITTEN, we have k = 3 or k = -3.

Answer 13

think of 3k = 9 as a statement saying

"3 times _____ equals 9"

what goes in the blank?

Answer 14

k ?

Answer 15

yes, but what number also goes in the blank in place of k?

Answer 16

3 times SOME NUMBER equals 9

what replaces "SOME NUMBER" ?

Answer 17

- 3 ?

Answer 18

why is it negative?

Answer 19

3 times -3 is positive 9 ? that's a true statement?

Answer 20

no ?

Answer 21

it's not

Answer 22

it should be 3 times 3 = 9

Answer 23

so the solution to 3k = 9 is k = 3

Answer 24

in a very similar fashion, the solution to 3k = -9 is k = -3

Answer 25

Another way to see that k = 3 is the solution to 3k = 9 is to divide both sides of 3k = 9 by 3 to isolate k

Answer 26

\[{-3 , 9 }\] ?

Answer 27

I don't know what you mean there. Are you saying the two answers are k = -3 and k = 9 ?

Answer 28

yea.

Answer 29

that's not correct

Answer 30

how did you get k = 9?

Answer 31

study guide , help

Answer 32

do you see how I got 3k = 9 and 3k = -9 ?

Answer 33

no , i really suck at math

Answer 34

go back to my steps and tell me where you got stuck

Answer 35

Then we use the idea that if |x| = p, then x = p or x = -p to go from this equation |3k| = 9 to these two equations 3k = 9 or 3k = -9

Answer 36

that part

Answer 37

that rule allows us to say things like

|x| = 7 turns into x = 7 or x = -7

Answer 38

or if |x| = 3, then x = 3 or x = -3

Answer 39

|x| = 3 means that some number x is 3 units away from zero

The numbers 3 and -3 are both 3 units away from zero, which is why the two answers to |x| = 3 are x = 3 or x = -3

Answer 40

so if I had |x| = 5, then what are the two solutions to x?

Answer 41

|x| = 5 or |x| = -5 ?

Answer 42

no, it should be x = 5 or x = -5

those two numbers are five units away from zero (on the number line)

Answer 43

absolute value is basically "distance the number is from zero on the number line"

Answer 44

what about something like |x| = 14

what are the two solutions to x?