more linear equations and consecutive integers

Question

Find three consecutive odd integers such that the sum of the smaller two is three times the largest increased by seven

Answer 1

Call the integers x, (x + 2), and (x + 4).

 

We can set up the following equation:

 

x + (x + 2) = 3(x + 4) + 7

 

2x + 2 = 3x + 12 + 7

 

2x + 2 = 3x + 19

 

2x = 3x + 17

 

-x = 17

 

x = -17

 

The numbers are -17, -15, and -13.