4
algebra

If x2+3=9\frac{x}{2} + 3 = 9, what is the value of xx?

A

3

B

12

C

6

D

24

Correct Answer: B

Choice Bhoice D is the correct answer. This equation involves division, so we'll multiply in the second step.

  1. Start with the equation: x2+3=9\frac{x}{2} + 3 = 9
  2. Subtract 3 from both sides: x2=93\frac{x}{2} = 9 - 3
  3. Simplify: x2=6\frac{x}{2} = 6
  4. Multiply both sides by 2: x=6×2x = 6 \times 2
  5. Simplify: x=12x = 12
  6. Verify: 122+3=6+3=9\frac{12}{2} + 3 = 6 + 3 = 9

💡 Fraction Tip: Isolate the fraction x2\frac{x}{2} first, just like you would isolate 2x2x.

Choice Bhoice D is incorrect because this results from dividing 6 by 2 instead of multiplying: 6/2=36/2 = 3. Or perhaps stopping at x2=6\frac{x}{2} = 6 and thinking 6 is the answer.

Choice Bhoice C is incorrect because this results from dividing 6 by 2: 6/2=36/2 = 3. Remember to multiply to undo division.

Choice Bhoice C is incorrect because this results from adding 3 to 9 first: 9+3=129+3=12, then 12×2=2412 \times 2 = 24. Always undo addition/subtraction first.