Question

Double checking: IS THIS RIGHT?

Prove that there exist a unique c that is an element of the real numbers such that x+cx=6. What must be the condition(s) on x so that c is defined?

x + cx = 6
Solve for c:
cx = 6-x
c=(6-x)/x, x can't equal 0.

Uniqueness:
x+c'x=6 x+c''x=6
c'x=6-x c''x=6-x
c'=(6-x)/x c''=(6-x)/x

c'=c'' therefore c is unique.

Answer 1

x(1+c) = 6

x not= 0 is a pretty good condition lol

Answer 2

and c not= -1

Answer 3

1 down and infinity to go :)