# Linear Equation 9

### From Homeworkwiki

**Find three consecutive integers such that the smallest integer plus one-fifth of the next minus half of the third integer gives 9**

**Solution:**

Let the smallest integer be x.

Therefore, the required three integers are x, x + 1 and x + 2.

Given, x + (x + 1) / 5 - (x + 2) / 2 = 9

=> [ 10 x + 2 (x + 1) - 5 (x + 2) ] / 10 = 9

=> 10 x + 2 x + 2 - 5 x - 10 = 90

=> 7 x = 90 + 8

i.e. x = 98 / 7 = 14

Therefore, the required consecutive integers are x, x + 1 and x + 2 = 14, 14 + 1 and 14 + 2

= **14, 15 and 16**