Question

How do you translate "the quotient of 14 and the difference between a number and -7 into an algebraic statement?

Answer 1

`14/(n-(-7))` or `14/(n+7)` where `n` is the number.

Explanation:

Let's do semantic analysis! Just kidding.

Let's break this down.
"The quotient of 14 and the difference between a number and -7"
This can be interpreted to be:

"The quotient of 14 and a number `a`"
Where `a` is the "difference between a number and -7"

So far we have `14/a`

Now, `a` is the "difference between a number and -7". Let's call this number `n`. `a` is the difference between `n` and -7 which is to say:
`a=n-(-7)`

Now we have these two statements:
`14/a`
`a=n-(-7)`

Let's put `a` back into its place:
`14/a=14/(n-(-7))`

Finally, we clear off the double negative and we get this statement:
`14/(n+7)`