Question

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Use the conditional statement to answer the question.

If 2x = 6, then x = 3.



Can the statement be written as a biconditional statement and why?

Yes, because the statement and its converse are both true
No, because the statement is false, but its converse is true
No, because the statement and its converse are both false
No, because the statement is true, but its converse is false

Answer 1

Yes, because the statement and its converse are both true.
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Answer 2

Answer: The correct option is

(A) Yes, because the statement and its converse are both true.

Step-by-step explanation: We are given the following conditional statement :

If 2x = 6, then x = 3.

We are to check if the above conditional statement can be written as a bi conditional statement with reason.

The converse of the given conditional statement is

If x = 3, then 2x = 6.

First let us consider that 2x = 6. Then, we get

`2x=6\\\\\Rightarrow x=(6)/(2)\\\\\Rightarrow x=3.`

Conversely, let x = 3, then we get

`2x=2*3=6.`

So, both the statement and its converse are TRUE.

Therefore, the statement can be written as a bi conditional statement as follows :

2x = 6 if and only if x = 3.

The answer is YES, because the statement and its converse are both true.

Thus, (A) is the correct option.