Question 1: The sum of twoconsecutive even integers is 22 less than 4 times the smaller of the two numbers. Find the larger of the two integers.

Lets first make a variable, x, which equals the small number. Consecutive integers means two numbers that follow up one another. In this example, it is 10/12, or 12/14, etc.

So, in order to make this an equation, it is (x)+(x+2), because the second number will be 2 larger than the first. The sum of that is 22 less than four times x, or the smaller integer. So, the equation set up is

X+x+2=4x-22

You then just solve that.

2x+2=4x-22

24=2x

x=12

So, the smaller number of the two is 12, which makes the larger integer 14.

I'll also do number 2 for you.

The sum of 3 consecutive even integers is 30 more than thesmallest integer. Find the largest integer.

We will again use x as the smallest integer.

x+(x+2)+(x+4)

This shows the consecutive even integers. And since this is 30 more than the smallest integer, we can turn that into an equation.

x+x+2+x+4-30=x

Then you simplify

3x-24=x

2x=24

x=12

The largest integer is 12+4, or 16.

Hoped it helped!