SOLUTION: The sum of twice a number and 3 less than the number is the same as the difference between -19 and the number . What is the number ?

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Question 1164055: The sum of twice a number and 3 less than the number is the same as the difference between -19 and the number . What is the number ?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
What is is help which you want here?

n, "a number"
2n%2B%28-3%2Bn%29=-19-n, or, 2n%2B%28-3%2Bn%29=abs%28-19-n%29 in case the first equation is inadequate.

Depending on what you really mean, either -4 or %2B11.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

There are two conceptions of the difference between the numbers.

Which one of these two conceptions do you prefer ?



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


the number: n
twice the number: 2n
3 less than the number: n-3
the sum of (twice the number) and (3 less than the number): (2n)+(n-3)

the difference between -19 and the number: -19-n

So

%282n%29%2B%28n-3%29+=+-19-n

Solve using basic algebra.

A comment about the response from one of the other tutors....

In everyday language, the difference between two numbers is nearly always interpreted as being a positive number. So the difference between 5 and 10 is 5, and the difference between 10 and 5 is 5.

However, in formal mathematics, the difference between A and B is ALWAYS A-B. So the difference between 5 and 10 is 5-10 = -5, and the difference between 10 and 5 is 10-5 = 5.

So in your problem "the difference between -19 and the number" is -19-n -- NOT n-(-19) = n+19.