How would I solve this:?

Question

Solve each (i.e., all solutions with verification that there are no others) in Z(subscript m) = {0,1,...,m-1}
2x + 4 = 7 in Z(subscript 11)
x^2 - 7x = 0 in Z(subscript 12)

I'm not very familiar with the notation and I'm not sure what I am being asked to do.
Also, if you know any good Discrete Mathematics websites please let me know.

Answer 1

Just guessing your question.

Z_m = {0, 1, ..., m-1}

This looks like a modulo set of base m

So, for

2x + 4 = 7 in Z_11

We need to find the solution for which the equation is true for modulo set of base 11

Consider x = 7,

2(7) + 4 = 18

Take modulo 11 (i.e. divide by 11 and take the remainder OR keep on taking away 11 until you get a number less than 11)

18 - 11 = 7

So the solution is x = 7, 7+11, 7+22, 7+33, ...

In general it is 7+11n

Answer 2

If that is the full question it looks as though you are being asked to solve some equations in either a different number base or when the calculation is made on a ring. so 2x+4 in Z(sub11) might mean modulo 11 and 2x would be 3 or 14 so x=1.5 or 7 would fit. It's possible that you use some convention which lets you assume that members of Z are positive integers or 0 so you could get a unique answer = 7.


Best of Luck - Mike

Answer 3

Z refers to a set of modulo sets

ie: Z(5): all X modulo 5

so 2x + 4 = 7 in Z(11) is looking for all solutions modulo 11

Answer 4

1.2x+4=7
2x=3
x=3/2

2.x^2-7x=0
x(x-7)=0
x=0 or 7

Answer 5

try this site
http://mathworld.wolfram.com/DiscreteMathematics.html