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The sum of a number...

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2 Answers

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?
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! ;)