6
algebra

If x+5=5x + 5 = 5, what is the value of xx?

A

5

B

10

C

1

D

0

Correct Answer: D

Choice Bhoice C is the correct answer. This is another special case where zero is the solution.

  1. Start with the equation: x+5=5x + 5 = 5
  2. Subtract 5 from both sides: x=55x = 5 - 5
  3. Simplify: x=0x = 0
  4. Verify: 0+5=50 + 5 = 5

This demonstrates the additive identity: adding zero to any number leaves it unchanged.

💡 Identity Property: For any number aa, we have a+0=aa + 0 = a. So when x+5=5x + 5 = 5, we know x=0x = 0.

Choice Bhoice C is incorrect because this confuses the constant (5) with the solution. Seeing the same number on both sides doesn't mean xx equals that number.

Choice Bhoice D is incorrect because this results from adding: 5+5=105 + 5 = 10. This is the wrong operation.

Choice Bhoice D is incorrect because some students might think "dividing the same numbers gives 1," but division isn't how we solve addition equations.