Answer:
the statement is not reversible
Explanation:
Hi there!
We are given the statement "if x=3, then x²=9"
In this case, the hypothesis (p) is x=3, while the conclusion (q) is x²=9
Reversing the statement would make it so that q is first, then p is after.
In other words, if the statement was originally "if p, then q", then the reverse of that statement would be "if q, then p"
This is known as the CONVERSE of the statement. Sometimes, the converse is true, but not always. If both the statement and the converse are true, then it's known as a BICONDITIONAL, where it works both ways
So we'll need to test if the following statement "if x²=9, then x=3" is true
If you subtract 9 from both sides, x²=9 becomes this equation:
x²-9=0
Using the square of differences formula, where x is a and 3 (square root of 9) is b:
(x-3)(x+3)=0
Now using zero product property:
x-3=0
Add 3 to both sides
x=3
AND:
x+3=0
Subtract 3 from both sides
x=-3
We see that the answers from this equation are x=3 and x=-3.
*if you plug 3 and -3 back in the equation, we can see they both work. Remember that x² is equal to x*x, or (x)²:
If x=3:
(3)²=9
(3)(3)=9
9=9
If x=-3:
(-3)²=9
(-3)(-3)=9
9=9
Hence, the statement doesn't work in the converse
The option "the statement is not reversible" is not the answer.
Hope this helps!