Answer:
56
Step-by-step explanation:
The sum of two <em>even</em> consecutive integers is 114.
Let's let the first even integer be 2n, where n is <em>some</em> integer: it doesn't matter what n is, but if we multiply n by 2, we are certainly getting an even number. This is because any integer multiplied by 2 is even.
So, this means that the second number is 2n+2.
Their sum is 114. In other words:
Solve for n.
Combine like terms:
Subtract 2 from both sides:
Divide both sides by 4:
So, n is 28.
This means that the first number is 28(2) or 56.
And the second number is 58.
So, the smallest integer is 56.
And we're done!