1

I have this question that is asking to find the value of x such that $x \equiv -6 (mod 5)$.

I have worked out the answer but the answer is not in the choices available to pick. This is why I decided to post this question to get a second opinion to see if I am right and if the question answer has error in it. The question provide 4 choices:

  1. 1
  2. 14
  3. 15
  4. 21

I worked my steps and concluded that x = -1. But there is no -1 here. I suppose the first choice may be -1 (perhaps the school mistake). What do you guys think?

Modified to show my working:

This working is based on what appear in my lecture notes, adjust to this question.

$x \equiv -6 (mod 5)$

$x - (-6) = 5k, k \in Z$

$x + 6 = 5$, where k = 1

$x = 5 - 6 = -1$

Edit 2:

It looks like the answer is 14. In lecture notes, it is mentioned that we can set k to any integer that will get $x \in N$. Subbing in 4 to k and multiply by 5 will result in 20. Take 20 minus 6 and the answer 14 is available.

Steven Alexis Gregory
  • 26,769
user3118602
  • 111

1 Answers1

1

It's asking: which one of these is a multiple of $5$ different from $-6$? Only one of the numbers given is so.

Prime Mover
  • 5,005
  • Hi, I have added my working steps to my original post. I am taken aback. What do your statement mean? My lecture notes show the way to find x based on the edited question I posted above. – user3118602 May 15 '20 at 14:23
  • One of them is different from $-6$ by a multiple of $5$. That is, $-6 - n = 5 k$. So is it $1$? No, $-6 - 1 = -7$. Is it $15$? No, $-6-15 = -21$. Is it $14$? Yes, because $-6-14 = -20$ which equals $-4 k$. – Prime Mover May 15 '20 at 14:31
  • Please check my edit 2 to see my assumption. Thanks! – user3118602 May 15 '20 at 14:31