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?

## 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

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! ;)