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# The sum of a number...

The sum of twice a number and 14 less than the number is the same as the difference between -26 and the number. What is the number?

### 2 Answers by Expert Tutors

Robert A. | Certified Teacher and Engineer - Tutoring Physics, Maths, and SciencesCertified Teacher and Engineer - Tutorin...
5.0 5.0 (114 lesson ratings) (114)
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There are 2 clauses here.  You need to translate each to maths language.
1) The sum of twice a number and 14 less than the number
2) is the same as the difference between -26 and the number
SO
1) The sum of twice a number and 14 less than the number
sum +      ( 2 x N )               ( N - 14 )
2) is the same as the difference between -26 and the number
=                              ( -26 - N )

Now remember the difference could be  (-26 - N)  or (N - (-26))
so you want the absolute value between them.
So the equation is:  ( 2 x N ) + ( N - 14 )  =  | -26 - N | or | N + 26 |
2N + N - 14 = |N+26|
3N = |N+26| + 14
can you take it from here?
Alexander F. | Patient and Passionate University of South Florida Math/Science TutorPatient and Passionate University of Sou...
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If we break this down, we can write this as a mathematical equation. It starts off by saying the sum, so it will be the sum of two quantities. Let's call the number we are solving for "x":

2x + (x-14)

It says that this sum is the same (or equal) as the difference of:

-26 - x

Let's set these equal to each other to complete the equation:

2x + (x-14) = -26 - x

3x - 14 = -26 - x

4x = -12

x = -3

To check the answer, you can plug x = -3 into the equation we developed earlier and if it's true (equal on both sides), then the answer checks out! ;)