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Is converse of a particulare algebraic equation TRUE?

Posted on 2012-09-21
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Consider following statement:

6x - 6 = x + 14 if x = 4

I come up with following conditional statement, inverse, converse, and contrapositive:

Conditional:               If x = 4, then 6x - 6 = x + 14                             TRUE

Inverse:                     If x != 4, then 6x - 6 != x + 14                           TRUE

Converse:                  If 6x - 6 = x + 14, then x = 4                             TRUE ?

Contrapositive:         If 6x - 6 != x + 14, then x != 4                            TRUE ?


How can we tell if converse if statement is TRUE when we don't know the value of x?  Another words how can we evaluate Converse if statment when we don't have the value of x?
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Question by:naseeam
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Bill Bach earned 2000 total points
ID: 38423707
You don't need the value of x.  Solving the equation 6x-6=x+14 returns exactly one value of x (4).
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