The larger of two consecutive integers is 7 greater than twice the smaller. Find the integers.

Solution:

Given, the larger of two consecutive integers is 7 greater than twice the smaller.

We have to find the integers.

Let the smaller integer be x.

The integers are consecutive.

Let the larger integer be x + 1.

Given, x + 1 = 7 + 2x

By grouping,

2x - x = 1 - 7

x = -6

So, x + 1 = -6 + 1 = -5

Verification:

x + 1 = 7 + 2x

LHS:

x + 1 = -6 + 1 = -5

RHS:

7 + 2x = 7 + 2(-6)

= 7 - 12

= -5

LHS = RHS.

Therefore, the integers are -6 and -5.

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The larger of two consecutive integers is 7 greater than twice the smaller. Find the integers.

Summary:

The larger of two consecutive integers is 7 greater than twice the smaller. The integers are -6 and -5.