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

1 Answer
May 24, 2017

Answer:

#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)#