Question 760719
Let the smaller even integer be n.

Then the next consecutive even integer is n+2 (because successive even numbers have a difference of 2)

Given that smaller + 3 times the bigger number gives sum of 46. We can write it algebraically as:

{{{n + 3*(n+2) = 46}}} ---- equation (1)

Expanding the brackets, we get

{{{n + 3*n + 6 = 46}}}

Adding like terms

{{{4*n + 6 = 46}}}

Subtracting 6 from both sides to get rid of the "6" on the left side

{{{4*n + 6 - 6 = 46 - 6}}}

{{{4*n = 40}}}

Dividing both sides by 4

{{{n = 40/4 = 10}}}

So the smaller number is 10 and the next number is 12. The two consecutive even integers are 10 and 12.

To check the answer, substitute n with 10 in equation (1)

{{{10 + 3*12 = 10 + 36 = 46}}}  ---> which is true.