10
algebra

If x+15=15x + 15 = 15, what is the value of xx?

A

1

B

0

C

15

D

30

Correct Answer: B

Choice Bhoice D is the correct answer. This final problem in the set demonstrates the additive identity once more.

  1. Start with the equation: x+15=15x + 15 = 15
  2. Subtract 15 from both sides: x=1515x = 15 - 15
  3. Simplify: x=0x = 0
  4. Verify: 0+15=150 + 15 = 15

The additive identity property states that 0+a=a0 + a = a for any number aa. When x+15=15x + 15 = 15, the only way this can work is if x=0x = 0.

💡 Identity Properties: Remember two key identities: a+0=aa + 0 = a (additive identity) and a×1=aa \times 1 = a (multiplicative identity). Here we use the first one.

Choice Bhoice D is incorrect because this results from adding instead of subtracting: 15+15=3015 + 15 = 30. This is the wrong operation.

Choice Bhoice C is incorrect because this confuses the constant (15) with the solution. Seeing 15 on both sides doesn't mean x=15x = 15; in fact, it means x=0x = 0.

Choice Bhoice C is incorrect because this confuses the multiplicative identity (1) with the additive identity (0). These are different concepts.