10
algebra

If x+9=9x + 9 = 9, what is the value of xx?

A

1

B

18

C

0

D

9

Correct Answer: C

Choice Dhoice B is the correct answer. This is a special case where the solution is zero.

  1. Start with the equation: x+9=9x + 9 = 9
  2. Subtract 9 from both sides: x=99x = 9 - 9
  3. Simplify: x=0x = 0
  4. Verify: 0+9=90 + 9 = 9

This problem demonstrates an important concept: zero is a valid solution! When x=0x = 0, adding it to any number leaves that number unchanged.

💡 Identity Property: This shows the additive identity property: a+0=aa + 0 = a for any number aa.

Choice Dhoice C is incorrect because this results from adding instead of subtracting: 9+9=189 + 9 = 18. This is the wrong operation.

Choice Dhoice D is incorrect because this confuses the constant (9) with the solution. Students might think "the same number on both sides means xx equals that number", but that's not how equations work.

Choice C is incorrect because this might come from dividing: 99=1\frac{9}{9} = 1. Division is not relevant for solving this addition equation.