(x)+(x+1)+(x+2)=51,
3x+3=51,
3x=51-3,
3x=48,
x=48/3,
x=16,
(x+1)=16+1=17,
(x+2)=16+2=18,
hence,16+17+18=51

Question: Three consecutive integers add up to 51. What are the integers? Explain in detail.

Solution:

To solve this problem, we need to find three consecutive integers whose sum is 51. Let's break down the problem into smaller steps:

Step 1: Define the variables:
Let's assume the first integer as 'x'. Since we are looking for consecutive integers, the second integer can be represented as 'x + 1', and the third integer can be represented as 'x + 2'.

Step 2: Write the equation:
The sum of the three consecutive integers is 51. Therefore, we can write the equation as:
x + (x + 1) + (x + 2) = 51

Step 3: Solve the equation:
Now, let's solve the equation to find the value of 'x':
x + x + 1 + x + 2 = 51
3x + 3 = 51
3x = 51 - 3
3x = 48
x = 48 / 3
x = 16

Step 4: Find the consecutive integers:
Now that we have found the value of 'x' as 16, we can substitute this value back into our assumption:
First integer: x = 16
Second integer: x + 1 = 16 + 1 = 17
Third integer: x + 2 = 16 + 2 = 18

Therefore, the three consecutive integers that add up to 51 are 16, 17, and 18.

Answer: The three consecutive integers that add up to 51 are 16, 17, and 18.