Question

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Answer 1

The answer sheet says
the odd integers are 15, 17, and 19.
I have no idea whats going on

Answer 2

You must NAME the three integers. Do that first.

Answer 3

x = first odd integer?

Answer 4

Good try, but it is only by luck that it will be odd. How do you REQUIRE it to be odd?

Answer 5

well

Answer 6

You don't have to go to that extent. Because they are consecutive odd integers, you know exactly what the difference is between the third one and the first one. Then the question becomes much simpler.

Answer 7

ohh yeah thats true

Answer 8

That may be true for this problem, but it is not a general solution to all such problems. Name the three odd integers.

Answer 9

Let the second odd integer be \(x\) and build a fairly simple equation based on the question.

Answer 10

A general solution is not required for a specific problem.

Answer 11

okay im gonna try and figure it out right now

Answer 12

A general solution is required for ALL problems. We can worry about esoterica later. If you are in a contest, where speed is of the essence, let's find all the speed-up, short cuts we can. When we are learning to be consistent, correct, and easily followed, please be more deliberate and distinct. Name the three integers.

Answer 13

would the third integer be 4?

Answer 14

Does that sound odd to you? What did you name the integers?

Answer 15

no it doesnt

Answer 16

How much is 3 times the difference between the 3rd and 1st odd integer?

Answer 17

ok first know that the sum and difference of two odd integers is even

Answer 18

Ah! Another single-problem solver.

Answer 19

now consider three consecutive odd integers 2x+1, 2x+3,2x+5

Answer 20

hmm

Answer 21

now can you solve it ?

Answer 22

yeah i can but how did you get it?
Three times the difference of the third and first odd integer is five less than the second odd integer so do you have to multiply or subtract?

Answer 23

what is that mean ?'' single-problem solver ''

Answer 24

Seriously, if you effectively name the integers, everything everyone is trying to tell you will be seen clearly before your eyes. To bad soha... did the naming for you. It would have been useful to have you come up with that.

Keep in mind that it is not the only definition. It could be 2x-1, 2x+1, 2x+3. You just have to keep track of your clear and useful definitions.

You were originally going for x,x+2,and x+4. That MIGHT work, but only if you get luck and find a solution where x is odd. With 2x+1, knowing that x is an integer, 2x+1 MUST be odd.

Answer 25

yes you can also consider these numbers as well

Answer 26

yeah.. uh

Answer 27

2x+1 is odd

Answer 28

1st odd integer: 2x+1
2nd odd integer: 2x+3
3rd oddineger: 2x+5

Build it from the problem statement.

Answer 29

yes

Answer 30

yeah i can do that.. but like im so lost on how you guys found the integers

Answer 31

We didn't FIND them. We just NAMED them.

Answer 32

oh okay

Answer 33

here first know this thing that odd integers are 1,3,5,7.....
now these are like 2x+1 here put any value of x you will get odd integer try it

Answer 34

okay got it :)

Answer 35

If you KNOW x is an integer, then 2x is an EVEN integer and 2x+1 is an ODD integer. That's all.

Answer 36

know you have to consider three consecutive odd integers so you can consider 2x+1,2x+3,2x+5 or 2x-1,2x+1,2x+3

Answer 37

another approach