SOLUTION: Find three consecutive even integers such that twice the sum of the first and third is twelve more than twice the second. My attempt: #1 = x #2 = x+2 #3 = x+4 2(x+x+4)

SOLUTION: Find three consecutive even integers such that twice the sum of the first and third is twelve more than twice the second. My attempt: #1 = x #2 = x+2 #3 = x+4 2(x+x+4) - 2

Question 50280: Find three consecutive even integers such that twice the sum of the first and third is twelve more than twice the second.
My attempt:
#1 = x #2 = x+2 #3 = x+4
2(x+x+4) - 2(x+2) =12
2x+2x+8 - 2x-4 = 12
2x-4 = 12
2x = 16
x = 8
x+2 = 10
x+4 = 12
The problem doesn't check so it's evidentally wrong, I'm thinking I set the problem up incorrectly. Can you please help me find my mistake or redirect me?
Thanks for your help.
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
Find three consecutive even integers such that twice the sum of the first and third is twelve more than twice the second.
Three consecutive even intergers:
First integer=x
Second integer = x+2
Third integer = x+4
.
Translation:
Twice the sum of the first and third: 2[(x)+(x+4)]
The "sum" means to add the first and third integer, than multiply the total by "2".
.
"is" means "equals"
.
Twelve more than twice the second: [(2)(x+2)]+12
Take the second integer (x+2), multiply it by "2" and add 12.
.
So, putting it all together:
2[(x)+(x+4)]=[(2)(x+2)]+12
2(2x+4)=(2x+4)+12
4x+8=2x+16
4x-2x+8=2x-2x+16
2x+8-8=16-8
2x=8
2x/2=8/2
x=4
.
Plug (x=4) into the integers and solve.
First integer=x=4
Second integer = x+2=4+2=6
Third integer = x+4=4+4=8
.
2[(x)+(x+4)]=[(2)(x+2)]+12
2(4+8)=(2)(6)+12
2(12)=12+12
24=24 [checks out]

RELATED QUESTIONS
Find three consecutive even integers such that twice the sum of the first and third is... (answered by bucky)

find three consecutive even integers such that twice the sum of the first and third is... (answered by richard1234)

Find three consecutive even integers such that twice the sum of the first and third... (answered by josmiceli)

find three consecutive even integers such that fives times the middle integer is twelve... (answered by josgarithmetic)

Find three consecutive even integers such that the sum of twice the first and three times (answered by math_tutor2020,josgarithmetic)

Find three consecutive even integers such that twice the sum of the first and third is... (answered by mananth)

Find three consecutive even integers such that the sum of the first and twice the second... (answered by jjordan95)

Find three consecutive even integers such that twice the sum of the second and third is... (answered by advanced_Learner)

find three consecutive odd integers such that the sum of the first and third is 33 more... (answered by ewatrrr)