Answer :

To find out which ordered pairs are equal, we need to evaluate both expressions at [tex]x = 5[/tex] and see if they yield the same result. Let's break it down.

For the first ordered pair [tex](\frac{5 - x}{x}, x - 5)[/tex]:

  1. Substitute [tex]x = 5[/tex] into the first part: [tex]\frac{5 - 5}{5} = \frac{0}{5} = 0[/tex].
  2. Substitute [tex]x = 5[/tex] into the second part: [tex]5 - 5 = 0[/tex].

So, the first ordered pair is [tex](0, 0)[/tex].

For the second ordered pair [tex](\frac{10 - x}{x - 5}, 2x - 10)[/tex]:

  1. Substitute [tex]x = 5[/tex] into the first part: [tex]\frac{10 - 5}{5 - 5} = \frac{5}{0}[/tex]. This is undefined because division by zero is not possible.
  2. Substitute [tex]x = 5[/tex] into the second part: [tex]2(5) - 10 = 10 - 10 = 0[/tex].

Since the first expression in the second ordered pair is undefined at [tex]x = 5[/tex], the pair does not evaluate to a number and cannot be equal to any numbers.

Therefore, when [tex]x = 5[/tex], [tex](0, 0)[/tex] from the first ordered pair is the only defined result.

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