What Are the Consecutive Even Integers in This Algebra Problem?

[mathdad]

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?

 

[topsquark]

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

 

[Wilmer]

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

No.
3x = 2x + 4 - 4
3x = 2x

Something's wrong with the problem itself...

 

[HallsofIvy]

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.

 

[Wilmer]

Ok ok...you really think 0 was intended?

Betya a Canadian Loonie that "4 more" was intended :)

 

[mathdad]

Is my equation right or wrong?

 

[Wilmer]

It's right for the way the problem is worded.

But I think the problem is not worded correctly.

 

[mathdad]

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.