MHB What Are the Consecutive Even Integers in This Algebra Problem?

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The discussion revolves around solving for two consecutive even integers based on the equation derived from the problem statement. The integers are represented as x and x + 2, with x being the smaller integer. The equation set up is 3x = 2(x + 2) - 4, which simplifies to 3x = 2x, leading to the solution x = 0. This indicates that the two integers are 0 and 2, although there is debate about whether the problem was worded correctly, with some suggesting "4 more" was intended instead of "4 less." The conclusion is that the integers derived from the equation are valid, but the problem's phrasing may be misleading.
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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