Question

Twelve less than four times a number is the same as six times the number. How do you find the number?

Answer 1

See a solution process below:

Explanation:

First, let's call the number we are looking for: `n`

Then:

"four times a number" can be written as `4n`

"Twelve less than" this would be written as `4n - 12`

"is the same as" gives us an equal sign: `4n - 12 =`

And "six times the number" finalizes the equation as:

`4n - 12 = 6n`

Next, subtract `color(red)(4n)` from each side of the equation to isolate the `n` term while keeping the equation balanced:

`-color(red)(4n) + 4n - 12 = -color(red)(4n) + 6n`

`0 - 12 = (-color(red)(4) + 6)n`

`-12 = 2n`

Now, divide each side of the equation by `color(red)(2)` to solve for `n` while keeping the equation balanced:

`-12/color(red)(2) = (2n)/color(red)(2)`

`-6 = (color(red)(cancel(color(black)(2)))n)/cancel(color(red)(2))`

`-6 = n`

`n = -6`