Find two consecutive even integers such that the smaller added to four times the larger gives a sum of 58.

10 & 12
There isn't a process beyond estimation and guessing / checking to solve this that I am aware of.

We need to make an equation. We know that the bigger number is 2 more than the smaller number. So let’s set up an equation.
X+2=Y; x is the smaller number and y is the bigger.
The smaller number added to four times the larger number is 58. We need another equation.
4(x+2)+x=58
We need x by itself so we can find one of the numbers. Let’s distribute.
4x+8+x=58
Add like terms
5x+8=58
Subtract 8.
5x=50
Divide.
50/5=10=x
If the smaller number is 10, the numbers are 10 and 12. Let’s check by plugging it into the equation.
4(12)+10=48+10=58

So, the numbers are 10 and 12.