Question

Write an inequality to represent the problem (1 pt.) and then solve the inequality by writing the pairs which solve it (1 pt.).
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.

Answer 1

can you just help me work my way to an answer please. . thanks

Answer 2

How do you represent two consecutive odd integers? Say m is your lesser odd integer. How do you represent the next odd integer?

Answer 3

n?

Answer 4

Well, sure, but that complicates things... Keep things in terms of m... (i.e. express it with only m as the unknown)

Answer 5

okay so you want a number?

Answer 6

Well, I want an expression... YOU need an expression. Tell me if you're stuck.

Answer 7

okay so m2=18?

Answer 8

\[m2\le18\] sorry i ment this

Answer 9

m2?
What do you mean by m2?

Answer 10

m times 2

Answer 11

Oh no, okay, my question was, if m is an odd integer, how would you express the next odd integer?

Say, your odd integer is 15. What's the next odd integer?

Answer 12

17

Answer 13

What about 23? What's the next?

Answer 14

25

Answer 15

How about 37?

Answer 16

39

Answer 17

See...
What did you do to 15 to get 17?
What did you do to 23 to get 25?
What did you do to 37 to get 39?

Answer 18

added 2

Answer 19

Precisely... so in general, if m is an odd integer, how do you express the NEXT odd integer?

Answer 20

add 2

Answer 21

so... the next odd integer is...?

Answer 22

i dont understand your question

Answer 23

I figured, what I wanted from you was to understand that
if
m
is an odd integer, the next odd integer is
m+2

Catch me so far?

Answer 24

so it would be o?

Answer 25

No, just m+2
The order of letters in the alphabet makes no difference in maths... divorce those two concepts, the sooner, the better.

Answer 26

okay so then what would i do

Answer 27

Just understand, for now
that
m is your odd integer
and the next odd integer
is
m+2
It MOST EMPHATICALLY does NOT mean two letters past m in the alphabet. Just plainly and simply m+2

Catch me so far?

Answer 28

yep

Answer 29

Just to make sure, if I were to ask you to represent three consecutive integers, with n being the first integer, how would you represent them?

Answer 30

m+3??

Answer 31

No. If n is an integer, what's the integer directly following it?

Answer 32

umm im not following

Answer 33

3 __ __

What are the two next integers?
How did you get them?

Answer 34

5 7
you add 2

Answer 35

two next INTEGERS
NOT
two next ODD integers.

Answer 36

so 4 5

Answer 37

Yes... how did you get them?

Answer 38

added 1

Answer 39

Okay, so what if you're given an arbitrary integer
n?

n __ __
What are the next two integers?

Answer 40

im not understanding what you mean do you want a nmumber or variables?

Answer 41

variables. numbers will never work.

Answer 42

so it would be o p

Answer 43

no... it has to be in terms of n~
You may only use the variable n.

Answer 44

n1 n2

Answer 45

n1?
n times 1?

Answer 46

n+1

Answer 47

and n+2.
I hope that much is clear to you.
Shall we continue with the problem?

Answer 48

yes

Answer 49

Okay, so it says two consecutive odd integers must have a sum less than or equal to 18...
What are our two consecutive odd integers again?

Answer 50

like 5 and 7 soo i added two

Answer 51

No, I meant our general odd integers
m and m+2

how would you express their sum?

Answer 52

oh okay i understand now thank you