The sum of a number...

Question

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?

Answer 1

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?

Answer 2

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! ;)