the biggest of 3 consecutive integers is half of the smaller number increased bey two find the numbers

if the three numbers are

x-1, x, x+1 then you know that

x+1 = (x-1)/2 + 2
or
x+1 = (x-1+2)/2

depending on how you parse the words

n-1 , n , n+1

n+1 = .5 (n-1) + 2
I guess, English not clear

n+1 = .5 n - .5 + 2

.5 n = .5

n = 1
so
0 , 1 , 2

To find the three consecutive integers, let's assign variables to represent the numbers. Let's assume the first number is 'x'.

According to the given information, the biggest number is half of the smaller number increased by two. So, the second number can be represented as '(x+2)/2'.

Since these are consecutive integers, the third number can be represented as '(x+2)/2 + 1'.

To verify, let's plug these values back into the equation:

x = first number
(x+2)/2 = second number
(x+2)/2 + 1 = third number

Now let's apply the information given. The biggest number, which is x, is equal to half of the smaller number increased by two:

x = (x+2)/2

To solve for x, we can cross-multiply:

2x = x + 2

Simplifying the equation:

2x - x = 2
x = 2

Now we know that the first number is 2. Plugging this into the equations for the second and third numbers:

Second number = (2+2)/2 = 4/2 = 2
Third number = (2+2)/2 + 1 = 4/2 + 1 = 2 + 1 = 3

Therefore, the three consecutive integers are 2, 2, and 3.