Find 3 consecutive even integers such that the sum of twice the smallest and three times the largest is 42

Answer:6, 8, 10Step-by-step explanation:Consecutive even integers are in the form:2, 4, 6 ... etcAs we can see, they have a "gap" of 2 in between. Thus, if we let the first number be "x", the next consecutive even number would be "x + 2" and the next one would be "x + 4".... and so on...We have our numbers:  x, x + 2, x + 4It says the sum of twice the smallest and 3 times the largest is 42. We can write:[tex]2x + 3(x+4) = 42[/tex]This is the equation. Now we solve for x and find all the 3 consecutive even integers. Shown below:[tex]2x + 3(x+4) = 42\\2x + 3x + 12 = 42\\5x = 42 - 12\\5x = 30\\x = \frac{30}{5}\\x=6[/tex]The 3 integers are 6, 8, and 10