Question

How do you write the algebraic expression given "the quotient of 14 and the difference between a number and -7"?

Answer 1

See a solution process below:

Explanation:

"the quotient" means to divide.

"the quotient of 14" means 14 is going to be divided by something. So we can write:

`14 -:`

The something it will be divided by is "the difference between a number and -7".

Lets call "a number" `n`.

"the difference" means we are going to subtract something from `n` and what we are going to subtract is a `-7`. We can write this as:

`n - (-7)`

Putting this together gives:

`14 -: (n - (-7))`

Or

`14/(n - (-7))`

Answer 2

`14/abs(n+7)`

Explanation:

The "quotient" just means the result of division.

I've interpreted the question with the following qualifications:

• "the quotient of ... and the difference...# means "the quotient of ... divided by the difference (as opposed to the quotient when the difference of ... is divided by 14)
• "the difference between a number and -7" means the absolute difference (it could mean the difference of a number minus -7; or the difference of a number subtracted from -7)

If we represent "a number" by the variable `n`
this gives us the answer shown above.