Math: Please check my Proofs.?

Question

Give a direct proof.
Let x be an integer. If 11x-5 is odd, then x is even.

Asuume 11x-5 is odd
11x-5= (2k+1)
so, x= 2k+1
11(2k+1)-5
22k+1-5 = 22k-4
Since 22k-4 is an integer 11x-5 is odd

Give an indirect proof.
Assume that x is odd. Then 2k+1 for some integer k
so, 11x-5= 11(2k+1)-5 = ? I am a bit confused with this one.


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Let x be an integer. Prove that 5x-11 is even if and only if x is odd.
Direct proof: Assume x is odd, then x=2k+1, for some integer k
so, 5(2k+1)-11 = 10k+5-11 = 10k-6= 2(5k-3)
Since (5k-3) is an integer, 5x-11 is even.

Assume x is even. Then x= 2l, for some integer l . Therefore, 5(2l)-11= 10l-11=
10l-12+1= 2(5l-6)+1
Since 5l-6 is an integer, 5x-11 is odd.
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Let x be an integer. Prove that x^3 is even if and only if x is even.

Proof: Assume that x is even. Then x=2k for some integer k.
Therefore, x^3=(2k)^3 = 8k^3= 2(4k^3)
Because 4k^3 is an integer, then integer k^3 is even.

For the Converse, assume x is odd. x=(2l+1), for some integer l.
x^3= (2l+1)^3= (2l+1)(2l+1)(2l+1)= 8l^3+12l^2+6l+1= 2(4l^3+6l^2+3l)+1
since (4l^3+6l^2+3l) is an integer, x^3 is even

Answer 1

parity(odd)(odd)=parity(even)
" (odd)(even)=parity(even)
" (even)(even)=parity(even)

x-y given both are even =even parity
" x odd and y odd =even parity
" x odd and y even =odd parity

Answer 2

Your evidence is real until you team. bear in mind, you attempt to get something of the from 2z+a million, so i might do here: observe a+b+c=2w+2x+2y+3 =2w+2x+2y+2+a million =2(w+x+y+a million)+a million observe that w+x+y+a million is an integer, say z for this reason 2(w+x+y+a million)+a million=2z+a million, that's extraordinary for this reason, the sum of three extraordinary integers is a wierd integer

Answer 3

i would help you, i really would, but i'm only a 8th grader in 9th grade math, and that question is really kinda IMPOSSIBLE.
good luck
:)

Answer 4

check your own proofs i hate geometry

Answer 5

too complicated question