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Let's solve the problem step by step.

The problem states:

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

Let the two consecutive integers be \( x \) (the smaller integer) and \( x + 1 \) (the larger integer).

According to the problem, the larger integer is 7 greater than twice the smaller integer. This gives us the equation:
\[
x + 1 = 2x + 7
\]

### Solving the equation:

1. Subtract \( x \) from both sides:
\[
x + 1 = 2x + 7 \implies 1 = x + 7
\]

2. Subtract 7 from both sides:
\[
1 - 7 = x \implies x = -6
\]

Now, since \( x = -6 \), the smaller integer is \(-6\), and the larger integer is:
\[
x + 1 = -6 + 1 = -5
\]

### Conclusion:
The two consecutive integers are \(-6\) and \(-5\).

Would you like further details or explanations?

Here are 5 related questions to deepen your understanding:
1. What is the general form of a pair of consecutive integers?
2. How can we verify that these integers satisfy the given condition?
3. Can we modify the condition and solve for a different relationship between the integers?
4. What happens if the difference between the larger and twice the smaller is a negative number instead of 7?
5. How can this type of problem be generalized to non-consecutive numbers?

**Tip:** When dealing with consecutive numbers, always express one in terms of the other, like \( x \) and \( x + 1 \), to simplify your equations.

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

Learn how to solve the problem of finding two consecutive integers where the larger is 7 greater than twice the smaller. This step-by-step solution includes key algebraic concepts and the use of linear equations. Suitable for Grades 7-9.

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