The sum of twice a number and 14 less than the number is the same as the difference between - 6 and the number. What is the number?

Question

The sum of twice a number and 14 less than the number is the same as the difference between - 6 and the number.  What is the number? 

 

Answer 1

Hi Kimberley, let x be the unknown number. The equation would look like this:

 

2x + (x - 14) = x - 6

 

Solve for x:

 

2x + (x - 14) = x - 6

 

2x + x - 14 = x - 6

 

3x - 14 = x - 6

 

Add 14 to both sides:

 

3x = x + 8

 

Subtract x from both sides:

 

2x = 8

 

Divide both sides by 2:

 

x = 4

 

Check:

 

2x + (x - 14) = x - 6

 

2 * 4 + (4 - 14) = 4 - 6

 

8 + 4 - 14 = -2

 

12 - 14 = -2

 

-2 = -2, numbers check.

 

Questions?

Answer 2

For this, you will need to set up an equation, by translating the sometimes-tricky words into symbols. Let's call "n" the number.

 

Twice the number = 2n.

14 less than the number = n - 14.

The sum of these = 2n + (n - 14). Simplified: 3n - 14

 

The difference between -6 and the number = n - (-6) = n + 6

 

Equate the two sides, and solve for n:

 

3n - 14 = n + 6

2n - 14 = 6

2n = 20

n = 10

 

The number is 10.