Question

Twelve less than a number is the same as 6, decreased by 8 times the number. What is the number?

Answer 1

The number is `color(purple)2`

Explanation:

Let x be the number.
Equation is `x-12=6-8x`
`x+8x=6+12`
`9x=18`
`x=2`

Answer 2

`n=2` (see explanation)
The number is 2.

Explanation:

Let's make the number `n` (variable). We're going to solve for `n` later.

"Twelve less than a number" `n-12`
"is the same as 6" `=6...`
"decreased by 8 times the number" `-8n`

"Twelve less than a number is the same as 6, decreased by 8 times the number" `n-12=6-8n`

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Ok, now we have to solve to find `n`...
First move everything with the variable to the left side.
`n\color(indianred)(+8n)-12=6\cancel(-8n)\cancel(\color(indianred)(+8n))`
`9n-12=6`

Now move all non-variable values to the right.
`9n\cancel(-12)\cancel(\color(slateblue)(+12))=6\color(slateblue)(+12)`
`9n=18`

Dividing to get the answer: `(\cancel(9)n)/\cancel(\color(seagreen)(9))=18/\color(seagreen)(9)`
`n=2`