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

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Answer 1 · 2017-08-02T11:53:32

See a solution process below:

"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 · 2017-08-02T11:53:55

$14/abs(n+7)$

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.