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

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Answer 1 · 2016-08-29T02:51:01

List an equation with the information supplied.

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

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

Since the larger number also equals $x + 1$ $x+1$

$x + 1 = 2 x + 7$ $x+1=2x+7$

Moving 'like' terms,

$- 6 = x$ $-6=x$

Now we plug $x$ $x$ to know the larger number

$- 6 + 1 = - 5$ $-6+1=-5$

and to certify this answer

$2 (- 6) + 7 = - 12 + 7 = - 5$ $2(-6)+7=-12+7=-5$

Bingo! The numbers are $- 6$ $-6$ and $- 5$ $-5$ .