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

Let’s denote the smaller integer as x. Since the integers are consecutive, the larger integer can be represented as x + 1.

According to the problem, the larger integer is 7 greater than twice the smaller integer. We can translate this into the equation:

x + 1 = 2x + 7

Now, let’s solve for x:

1. Start by simplifying the equation:
2. Subtract x from both sides:
• 1 = x + 7
3. Next, subtract 7 from both sides:
• 1 – 7 = x
• -6 = x

Now that we have found x, which is -6, we can determine the two consecutive integers:

• Smaller integer: -6
• Larger integer: -5

To verify it, we can check if the larger integer (-5) is indeed 7 greater than twice the smaller integer (-6):

• Twice the smaller integer: 2 * (-6) = -12
• 7 greater than that: -12 + 7 = -5

This confirms our solution. Therefore, the two consecutive integers are -6 and -5.