What Are the Consecutive Even Integers in This Algebra Problem?

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Discussion Overview

The discussion revolves around solving an algebra problem involving two consecutive even integers. Participants explore the setup of the problem, the formulation of the equation, and the implications of the solution derived from it.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants propose that the two consecutive even integers can be represented as x and x + 2, where x is the smaller integer.
  • There is a formulation of the equation as 3x = 2(x + 2) - 4, which some participants confirm as correct.
  • One participant suggests that x should be even and offers the alternative of setting x = 2n to ensure the solution remains even.
  • Another participant challenges the correctness of the equation, stating that it simplifies to 3x = 2x, implying a potential issue with the problem itself.
  • There is a discussion about the validity of the solution x = 0, with one participant asserting that it is a valid even integer and another questioning if this was the intended solution.
  • Some participants express skepticism about the wording of the problem, suggesting it may not be correctly framed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the problem's wording or the intended solution. Multiple competing views remain regarding the interpretation of the equation and the validity of the derived solution.

Contextual Notes

There are unresolved assumptions regarding the problem's wording and the implications of the solution x = 0. The discussion reflects differing interpretations of the mathematical setup.

mathdad
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Three times the smaller of two consecutive EVEN integers IS four less than twice the larger. What are the two integers?

My set up:

x and x + 2 are the two consecutive even integers. True?

Here, x is the smaller integer and (x + 2) the bigger integer. True?

The equation is 3x = 2(x + 2) - 4. Yes?
 
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RTCNTC said:
Three times the smaller of two consecutive EVEN integers IS four less than twice the larger. What are the two integers?

My set up:

x and x + 2 are the two consecutive even integers. True?

Here, x is the smaller integer and (x + 2) the bigger integer. True?

The equation is 3x = 2(x + 2) - 4. Yes?
Yup. And make sure that x is even. I don't recall if I made a previous comment to you or someone else... If you like you can set x = 2n in your equations and you will come up with a solution that has to be even. But there is no requirement to do so.

-Dan
 
RTCNTC said:
The equation is 3x = 2(x + 2) - 4. Yes?
No.
3x = 2x + 4 - 4
3x = 2x

Something's wrong with the problem itself...
 
Wilmer said:
No.
3x = 2x + 4 - 4
3x = 2x

Something's wrong with the problem itself...
Why? 3x- 2x= x= 0 is a perfectly valid solution. 0 is an even number, the next even number is 2, 3 times 0 is 0, 2 times 2 minus 4 is also 0.
 
Ok ok...you really think 0 was intended?

Betya a Canadian Loonie that "4 more" was intended :)
 
Is my equation right or wrong?
 
It's right for the way the problem is worded.

But I think the problem is not worded correctly.
 
My set up:

x and x + 2 are the two consecutive even integers.

Here, x is the smaller integer and (x + 2) the bigger integer.

The equation is 3x = 2(x + 2) - 4.

3x = 2(x + 2) - 4

3x = 2x + 4 - 4

3x = 2x

3x - 2x = 0

x = 0

One of the integers is 0 and the other is 0 + 2 or 2.
 

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