Question

please help!

The product of 9 and a number is 12 less than three times that number.

What is the number?

Answer 1

@TheSmartOne @AriPotta

Answer 2

`The product of 9 and a number`
Well, `product` is the result of what operation?

Answer 3

Multiplication

Answer 4

Okay so `The product of 9 and a number` would be \(9\times n\).

Answer 5

`is` this is just equality \(=\)

Answer 6

`12 less than three times that number`
In this case `less` is an operation. It is subtraction.

Answer 7

`three times that number` will be \(3\times n\)
`12 less than three times that number` will be \(3\times n-12\).

Answer 8

All together:\[
9\times n = 3\times n - 12
\]

Answer 9

Can you solve for \(n\)?

Answer 10

4...?

Answer 11

Or -4 maybe

Answer 12

What was your first step in simplifying?

Answer 13

By the way \(3\times n\) can be written as \(3n\). We can write it as \[
9n=3n-12
\]

Answer 14

If you put \(n=-4\), then you get:\[
9(-4) = 3(-4)-12\\
-36=-12-12\\
-36=-24
\]This is not correct. We should solve for \(n\) using algebra.

Answer 15

Do you need a hint?

Answer 16

Yeah

Answer 17

Well, we want \(n\) to be on only one side, and so we can use subtraction to get rid of \(3n\) from the right side.

Answer 18

Okay

Answer 19

Do you know what the result is when you do that?

Answer 20

No :/

Answer 21

\[
\underbrace{9n}_{-3n} = \underbrace{3n-12}_{-3n}
\]

Answer 22

Left side:\[
9n-3n = (9-3)n = 6n
\]

Answer 23

Right side: \[
3n-12-3n = (3-3)n-12 = 0n-12=-12
\]The \(3n\) goes away as planned.

Answer 24

So we have\[
6n=-12
\]

Answer 25

-2?

Answer 26

Yes

Answer 27

Thank you for explaining it to me yay :) @wio