10
algebra

If x25=0x - 25 = 0, what is the value of xx?

A

1

B

0

C

-25

D

25

Correct Answer: D

Choice Ahoice D is the correct answer. When an equation equals zero, we still use the same solving strategy.

  1. Start with the equation: x25=0x - 25 = 0
  2. Add 25 to both sides: x=0+25x = 0 + 25
  3. Simplify: x=25x = 25
  4. Verify: 2525=025 - 25 = 0

This problem demonstrates that when we subtract a number from itself, we get zero: aa=0a - a = 0.

💡 Zero Property: The equation xa=0x - a = 0 always has the solution x=ax = a. This is because only when x=ax = a will xa=0x - a = 0.

Choice Ahoice C is incorrect because zero is the result of the equation, not the value of xx. The right side being zero doesn't mean x=0x = 0.

Choice Ahoice D is incorrect because this is the negative of the correct answer. Some students might incorrectly think x=25x = -25 makes the expression zero.

Choice Ahoice C is incorrect because this might come from treating the problem as division: "25 divided by something equals 0 can't work, so maybe 1?" This reasoning is flawed.