SOLUTION: Homework from Algerbra I book Define a variable, write an equation and solve each problem three times the greatest of three consecutive even intergers exceed twice the least

Algebra ->  Expressions-with-variables -> SOLUTION: Homework from Algerbra I book Define a variable, write an equation and solve each problem three times the greatest of three consecutive even intergers exceed twice the least      Log On


   

Question 226257: Homework from Algerbra I book
Define a variable, write an equation and solve each problem
three times the greatest of three consecutive even intergers exceed twice the least by 38. Find the intergers
I started with x, x+2, x+4 for the consecutive even intergers
3(x+4) + 2x +38 but then I get lost and don't know what the equation is

Found 2 solutions by jim_thompson5910, LtAurora:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=first consecutive even integer, x+2=second consecutive consecutive integer, x+4=third consecutive even integer.

We're also going to assume that all of these integers are positive. So the third is the largest.


Since "three times the greatest of three consecutive even integers exceed twice the least by 38", we get the translation 3%28x%2B4%29=2x%2B38



3%28x%2B4%29=2x%2B38 Start with the given equation.


3x%2B12=2x%2B38 Distribute.


3x=2x%2B38-12 Subtract 12 from both sides.


3x-2x=38-12 Subtract 2x from both sides.


x=38-12 Combine like terms on the left side.


x=26 Combine like terms on the right side.


----------------------------------------------------------------------

Answer:

So the solution is x=26 which means that the first number is 26, the next number is 26+2=28, and the third is 26+4=30

Answer by LtAurora(115) About Me  (Show Source):
You can put this solution on YOUR website!
On the right track:
3%28x%2B4%29=2x%2B38
Then solve:
3x%2B12=2x%2B38 Distribute the 3.
3x=2x%2B26 Move the 12 by subtracting it.
x=26 move the 2x by subtracting it.
So, the 3 integers are 26, 28, 30.