Question

Find x if y = –4.

Answer 1

http://media.education2020.com/evresources/2003-05-04-00-00_files/i0070000.jpg

Answer 2

you guys just love typing then not saying anything

Answer 3

We can plug in that value of y=-4 into our equation:
\( \displaystyle 3\color{blue}y - \dfrac{6}{x} = 12 \)
\( \displaystyle 3\left( \color{blue}{-4} \right) - \dfrac{6}{x} = 12 \)
Now we need to take steps to simplify and get x all by itself. Do you have ideas on some steps that might help us?

Answer 4

multiply 3 and 4 ?

Answer 5

Yep, that would help.
-12 - 6 / x = 12.
So now we can add, subtract, multiply, and divide things to get x alone. For example, adding that 12 to both sides:
-12 - 6 / x + 12 = 12 + 12
- 6 / x = 24

Answer 6

multiply -6 and 12?

Answer 7

24*

Answer 8

Are you familiar with "cross multiplying"? Since multiplying both sides by -6 or 24 won't help with that x in the bottom.

Answer 9

ah so then what do we do ?

Answer 10

multiply 24 into x and 6 into what ?

Answer 11

It would just be a 1, because 24/1 doesn't change its value. We can always take a regular number over 1 like this:
\( \dfrac{-6}{x} = \dfrac{24}{1} \)
\( 24 x = -6 \color{gray}{\times 1} \)
Lastly, we just have a coefficient on x. We want to divide both sides by 24, and with a little simplification we will be done. :)

Answer 12

so 6 into 24 or 24 into 6?

Answer 13

Divide both sides by 24. Doing so does not change equality since we've done the same thing to both sides, and it cancels with the 24 multiplied onto x (which we wanted to get alone, so it is good!)

\( \dfrac{\cancel{24} x}{\cancel{24}} = \dfrac{-6}{24} \) x = -6/24

Answer 14

thanks

Answer 15

you're welcome!