Question

Two times the greater of two consecutive integers is 9 less than three times the lesser integer. What are the integers?

Answer 1

The consecutive integers are `11 and 12` .

Explanation:

The integers can be written as `x and x+ 1`

The larger of the integers is `x+1` so the first expression is

`2 xx ( x+1)`

The smaller of the integers is `x` so the second expression is

`3 xx x - 9`

These two expressions can be set equal to each other

`2 xx ( x+1) = 3 xx x -9 " "` multiply 2 across `( x + 1)` so

`2x + 2 = 3x -9" "` Add 9 to both sides of the equation

`2x + 2 + 9 = 3x -9 + 9" "` results into

`2x + 11 = 3x" "` subtract `2x` from both sides of the equation

`2x - 2x + 11 = 3x - 2x" "` results into

`11 = x`

`x` is the smaller integer which is `11`

`x+ 1` is the larger integer which is `12`