SOLUTION: find three consecutive even integers such that twice largest integer exceeds the sum of the sum of the first two by 6.

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Question 224489: find three consecutive even integers such that twice largest integer exceeds the sum of the sum of the first two by 6.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find three consecutive even integers such that twice largest integer exceeds the sum of the sum of the first two by 6.

Step 1. Let n be the first even integer.

Step 2. Let n+2 and n+4 be the next two even integers.

Step 3. Let 2(n+4)=2n+8 be twice the largest integer.

Step 4. Let n+n+2=2n+2 be the sum of the first two.

Step 5. Then, 2n+8=2n+2+6 since twice largest integer exceeds the sum of the sum of the first two by 6.

Step 6. Solving the equation in Step 5 yields the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: Equation 2n%2B8=2n%2B2%2B6 was fully solved.
  • Text form: 2n+8=2n+2+6 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2n%2B8=2n%2B2%2B6+%29
    For tutors: simplify_cartoon( 2n+8=2n+2+6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2An%2B8=2%2An%2Bhighlight_red%28+2+%29%2Bhighlight_red%28+6+%29.
Added fractions or integers together
It becomes 2%2An%2B8=2%2An%2Bhighlight_green%28+8+%29.
Look at 2%2An%2B8=highlight_red%28+2%2An%2B8+%29.
Moved these terms to the left highlight_green%28+-2%2An+%29,highlight_green%28+-8+%29
It becomes 2%2An%2B8-highlight_green%28+2%2An+%29-highlight_green%28+8+%29=0.
Look at 2%2An%2Bhighlight_red%28+8+%29-2%2An-highlight_red%28+8+%29=0.
Added fractions or integers together
It becomes 2%2An%2Bhighlight_green%28+0+%29-2%2An=0.
Look at 2%2An%2Bhighlight_red%28+0+%29-2%2An=0.
Moved 0 to the right of expression
It becomes 2%2An-2%2An%2Bhighlight_green%28+0+%29=0.
Look at 2%2An-2%2An%2Bhighlight_red%28+0+%29=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes 2%2An-2%2An=0.
Look at highlight_red%28+2%2An+%29-highlight_red%28+2%2An+%29=0.
Eliminated similar terms highlight_red%28+2%2An+%29,highlight_red%28+-2%2An+%29 replacing them with highlight_green%28+%282-2%29%2An+%29
It becomes highlight_green%28+%282-2%29%2An+%29=0.
Look at highlight_red%28+%282-2%29%2An+%29=0.
Since highlight_red%28+%282-2%29%2An+%29 has zero as a factor, it should be replaced with a zero
Look at 0=0.
Added fractions or integers together
It becomes 0=0.
Result: 0=0

Universal Simplifier and Solver


Done!



Step 7. ANSWER: The three consecutive integers can be anything that the satisfies equation in Step 5.

For example 2, 4, 6 will yield 2(6)=2+4+6 which is a true statement

Another example, 20, 22, 24 will yield 2(24)=20+22+6 which is another true statement

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J