divisibility

[carolina.gholmia]

I am trying to solve this but am not sure about the answer.

if 4x - 11 = 6y - 5, and we are given that x and y are non-zero integers and that (6y-5) is divisible by 11, is x/11?

(4x-11)/11 = 4x/11 - 1. if 4x is divisible by 11, does it necessarily proceed that x/11?

if x = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (and their negative counterparts), the expression will not be an integer. so the smallest non-zero integer x can be is +/- 11. same for 12, 13, 14, 15...

i would guess that that proves x is divisible by 11, but is there something i am forgetting or assuming that isnt necessarily true?

thank you!

[shubham_sagijain]

I am trying to solve this but am not sure about the answer.

if 4x - 11 = 6y - 5, and we are given that x and y are non-zero integers and that (6y-5) is divisible by 11, is x/11?

(4x-11)/11 = 4x/11 - 1. if 4x is divisible by 11, does it necessarily proceed that x/11?

if x = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (and their negative counterparts), the expression will not be an integer. so the smallest non-zero integer x can be is +/- 11. same for 12, 13, 14, 15...

i would guess that that proves x is divisible by 11, but is there something i am forgetting or assuming that isnt necessarily true?

thank you!

Caroline,
Your approach looks correct to me...Infact, i also solved on similar lines..

If we know that (6y - 5) is divisible by 11, then we know that (4x-11) will also be divisible by 11..
When you are adding or subtracting the same divisor (in this case +/- 11) from any number (in this case 4x), then that number (in this case 4x) must be divisible by 11...
so, that proves 4x to be divisible by 11 which in turn proves that x is divisible by 11 as you cannot factor the denominator (in this case 11, the prime number)..

hope the explanation above helps..

Thanks,
Shubh

[aanaandaa1]

Since x needs to be a factor of 11 to make this expression (4x - 11) divisible by 11, so I think x is divisible by 11.

I guessed- since (6y - 5) is divisible by 11, so (4x - 11) too must be divisible by 11

[jnelson0612]

Great work! Everyone here is correct. Please let us know if you need further explanation. :-)