Help with this word equation?

Question

Okay, here's the question. Find three consecutive even integers such when the third is subtracted from the first, the answer is negative four.

Now, don't use your head, because I've spent an hour thinking this through, and I know it can be any three consecutive even integers, but I want to know how to solve the equation.

All I've got so far is...

b= 1st integer
b+2= 2nd integer
b+4= 3rd integer

b - b + 4 = -4

And that's where I'm stuck! Help please!

Answer 1

Hi,

I think you've got the right idea. Your equation should actually read
b - (b+4) = -4
then,
b - b -4 = -4
-4 = -4

so the equation is always true for any value of b.

and if you think about it, there are infinitely many answers because if you take only the even intergers, the difference between the largest and smallest will always be 4. (or in the language of this question the difference between the smallest and the largest will be -4)

I'm not sure if you have a trick question, or if something is lost in translation.

Hope that helps,
Matt

Answer 2

-6, -4, -2 >> such as when the third is subtracted from the first -6 -(-2) = -6 +2 = -4.
or -8, -6, -4 or -10, -8, -6 or -12, -10, -8 ...
the question wants you to think about the negative integers. Any three consecutive negative integers are ok for this question. But you should take the first as the smallest one, so that it obeys the rule. eg. -6 is the first one -6+2 is the second -6+4 is the third one.

Answer 3

so 4 = -4 !!
equation doesn't hold
that is because if b is an integer, b+2 is not consecutive!

what you do is this:
b= 1st integer
b+1= 2nd integer
b+2= 3rd integer
for the result to happen:
b - (b+2) = -4 so 2 = -4 !!!
so we know this can never be true.
Infact the result is always = -2 for any 3 consecutive integers

Answer 4

Let the 3 consecutive even integers be
x, x+2, x + 4

x + x + 2 - (x + 4) = - 4

2x + 2 - x - 4 = - 4

x - 2 = - 4

x = - 2

So the integer value is - 2

Answer 5

b - (b + 4) = b - b - 4 = -4, which gives you -4 = -4, which is always true.

Therefore, any 3 consecutive even integers will have this property.

Answer 6

You did not distribute the negative. It should be: b-(b+4) = -4 ,
b-b-4 = -4, -4 = -4. Because the answer is true, -4=-4, that means that there is an infinite number of answers.