Consecutive Integers     

The sum of three consecutive integers is 528. 
The smallest integer among the three integers is? 

x = 1st consecutive integer
x + 1 = 2nd consecutive integer
x + 2 = 3rd consecutive integer 

x + x + 1 + x + 2 = 528 {sum of three consecutive integers is 528}
3x + 3 = 528 {combined like terms}
3x = 525 {subtracted 3 from both sides}
x = 175 {divided both sides by 3}
x + 1 = 176 
x + 2 = 177 

smallest is 175 

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Number problem with quadratic equation

If 6 is added to the square of a number, the result is 22.
Find all such numbers.

x² + 6 = 22 {six added to the square of a number results in 22}
x² = 16 {subtracted 6 from both sides}
x = 4 or - 4 {took square root of both sides} 

the possible numbers are 4 or - 4 

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Consecutive integers

The sum of three consecutive integers is 25 larger than
twice the smallest integer. Find the integers. 

 x = 1st consecutive integer
x + 1 = 2nd consecutive integer
x + 2 = 3rd consecutive integer 

x + x + 1 + x + 2 = 2x + 25 
{sum of the three is 25 larger than twice the smallest}

3x + 3 = 2x + 25 {combined like terms}
x + 3 = 25 {subtracted 2x from both sides}
x = 22 {subtracted 3 from both sides}
x + 1 = 23 {substituted 22, in for x, into x + 1}
x + 2 = 24 {substituted 22, in for x, into x + 2} 

22, 23, and 24 are the three consecutive integers 

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