# The larger of two consecutive integers is 7 greater than twice the smaller. What are the integers?

Aug 29, 2016

List an equation with the information supplied.

#### Explanation:

Consecutive integers are just 1 apart, so let's say our smaller integer is $x$ and the larger is

$2 x + 7 \to 7$ greater than twice the smaller number

Since the larger number also equals $x + 1$

$x + 1 = 2 x + 7$

Moving 'like' terms,

$- 6 = x$

Now we plug $x$ to know the larger number

$- 6 + 1 = - 5$

$2 \left(- 6\right) + 7 = - 12 + 7 = - 5$
Bingo! The numbers are $- 6$ and $- 5$.