Question

How do you find three consecutive even integers such that the sum of twice the first and the third is 2 less than three times the third integer?

Answer 1

The numbers are 2, 4 and 6

Explanation:

So, we want 3 consecutive even integers. We can represent them by the following notations:

`x`, `x+2` and `x+4`

Now for our equation:

• The sum of twice the first and the third:
  `2x+2(x+4)`
• Two less than three times the third:
  `3(x+4)-2`

Now we set those two equal to each other and solve for `x`
`2x+2(x+4)=3(x+4)-2`

`2x+2x+8=3x+12-2larr` expanding both sides

`4x+8=3x+10larr` adding the `x`'s and numbers

`4x-3x=10-8larr` subtracting both sides by `-3x` and `-8`

`x=2`

So our other two numbers are:
`x+2=4" "` and `" "x+4=6`