Converse of a statment

Question

Hello,

I really struggle with these types of problem, could you tell me if this is correct.

If, x+3 = 10/x ⇒ x = 2

What is the converse of this statement?

Is the original statement true? Also is the converse true?

My answer,

The converse is, x = 2 ⇒ x+3 = 10/x

The original statement is false, because -5 is also a solution.

"Am i right in thinking if 2 is not the only solution the the statement is false, it would only be true if x=2 was the only solution"

The converser is also false, this is because x = 2 is not only true by x +3 = 10/x it is true for other things, for example, we could have x + 5 = 14/x.

Am i right in thinking for the converse to be true it can only be true if x +3 = 10/x is the only way x can equal 2, which of course is not, hence i just need to provide a counterexample as i did?

Thank you so much

Lucy

Answer 1

Ok, so actually the original statement is false because we are leaving out a factor, -5. Meanwhile, the converse is actually true because you're already setting x=2, so it blends over to the next statement, x+3=10/x, so the converse is actually true. I hope that helped you!