SOLUTION: Picture yourself in a ’special’ world where x = -x Under this assumption, select the true statement/s: A) Every 2x can be ’exchanged’ for 0 B) Every 5x can be ’exchange

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Question 1151424: Picture yourself in a ’special’ world where x = -x Under this assumption, select the true statement/s:
A) Every 2x can be ’exchanged’ for 0
B) Every 5x can be ’exchanged’ for x
C) Every x can be ’exchanged’ for -x
D) x + x + x can be ’exchanged’ for x + x + -x
E) Every 3x can be ’exchanged’ for x
F) Every 3x can be ’exchanged’ for 2x + x
G) None of these
Note: can you please show me a solution not just the letters of the right answers, I want to know how to solve this type of questions. Thanks

Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if x+=+-x then:
A) Every 2x can be ’exchanged’ for 0-> false 2x can be ’exchanged’ for 2%28-x%29=-2x
B) Every 5x can be ’exchanged’ for x-> false 5x can be ’exchanged’ for 5%28-x%29=-5x
C) Every x can be ’exchanged’ for -x-> true
D) x+%2B+x+%2B+x can be ’exchanged’ for x+%2B+x+%2B+%28-x%29-> false x%2Bx%2Bx can be ’exchanged’ for %28-x%29%2B%28-x%29%2B%28-x%29=-x-x-x=-3x
E) Every 3x can be ’exchanged’ for x-> false 3x can be ’exchanged’ for 3%28-x%29=-3x
F) Every 3x can be ’exchanged’ for 2x+%2B+x-> false 3x can be ’exchanged’ for 2%28-x%29%2B%28-x%29=-2x-x=-3x
G) None of these


answer:
C) Every x can be ’exchanged’ for -x

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
2x becomes 2(-x) or -2x. That only works when x=0, so in general it does not work
5x becomes -5x, and that is not x
x can be exchanged for -x by definition, for it is given
x+x+x can be exchanged for x+x+-x, since x can be exchanged for -x
2x+x=3x, so this exchange works. It would also work for 2x+ -x, although that is not asked.