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

A) 4,5
B) -8,-9
C) -5,-6

integer 1 = a

integer 2 = b

b-a = 1 (b is one more than a)
b-7 = 2*a (b is seven more than two times a)

a = b-1
b-7 = 2*(b-1)
b-7 = 2b-2
b = -5

so a should be -6

answer is C)

To solve this problem, let's first define our variables. Let's call the smaller integer x, and the larger integer (which is 7 greater than twice the smaller) y.

From the given information, we have two conditions:
1. The larger integer is 7 greater than twice the smaller: y = 2x + 7.
2. The two integers are consecutive, which means that the larger integer is one more than the smaller: y = x + 1.

Now, we can set up a system of equations using these conditions:
Equation 1: y = 2x + 7
Equation 2: y = x + 1

Since both equations are equal to y, we can set them equal to each other:
2x + 7 = x + 1

Next, let's solve for x by subtracting x from both sides of the equation:
2x - x + 7 = x - x + 1
x + 7 = 1

To isolate x, we'll subtract 7 from both sides of the equation:
x + 7 - 7 = 1 - 7
x = -6

Now that we have x, we can substitute this value back into one of the original equations to find y.

Using Equation 2: y = x + 1
y = -6 + 1
y = -5

So, the two consecutive integers are -6 and -5.

Therefore, the correct answer is C) -5, -6.

Let's represent the smaller integer as "x" and the larger integer as "x+1".

According to the given information, we can set up the equation:

x+1 = 2x + 7

Now, let's solve for x:

x+1 = 2x + 7

Subtracting x from both sides:

1 = x + 7

Subtracting 7 from both sides:

-6 = x

So, the smaller integer is -6 and the larger integer is -6 + 1 = -5.

Therefore, the answer is option C) -5,-6.