Question

twice a number is 12 less than 6 times the opposite of the number. find the number.

Answer 1

let the number is x
then
2x -12 = -6x

Answer 2

so do I subtract 2 from 6 then?

Answer 3

no
add 2x and 6x

Answer 4

that would be -4x since the 6 is negative

Answer 5

ok let me make it easy for you
2x - 12 = -6x
2x +6x = 12

Answer 6

now find x

Answer 7

would that be 8x=12? or am I doing this all wrong..

Answer 8

And you would see that you set it up incorrectly....all the other steps are correct....however it should have been set up as

\[2x = -6x - 12\]

From what you are doing...you will get 3/2 correct? when you plug that in to check...it is incorrect....

Answer 9

okay. thank you

Answer 10

So....start again from this equation

\[2x = -6x - 12\]

add 6x to both sides...this will move that -6x to the left side...and make it positive ...so

\[8x = -12\]

now you divide both sides by 8

\[x = -\frac{ 12 }{ 8 }\]

when simplified...

\[-\frac{ 3 }{ 2 }\]

Now...we check it back in the original equation

\[2(-\frac{ 3 }{ 2 }) = -6(-\frac{ 3 }{ 2 }) - 12\]
\[-3 = 9 - 12 \]
\[-3 = -3\]

so -(3/2) would be your answer