10
algebra

If x2+x3>10\frac{x}{2} + \frac{x}{3} > 10, what is the solution?

A

x>12x > 12

B

x>6x > 6

C

x>60x > 60

D

x>5x > 5

Correct Answer: A

Choice A is the correct answer. Combine fractions using a common denominator.

  1. LCD of 2 and 3 is 6: Multiply all terms by 6.
  2. Multiply: 6(x2)+6(x3)>6(10)6(\frac{x}{2}) + 6(\frac{x}{3}) > 6(10)
  3. Simplify: 3x+2x>603x + 2x > 60
  4. Combine: 5x>605x > 60
  5. Divide by 5: x>12x > 12

?�� Strategic Tip: Alternatively, x2+x3=3x6+2x6=5x6\frac{x}{2} + \frac{x}{3} = \frac{3x}{6} + \frac{2x}{6} = \frac{5x}{6}. Then 5x6>105x>60x>12\frac{5x}{6} > 10 \rightarrow 5x > 60 \rightarrow x > 12.

Choice B is incorrect because it might come from adding denominators (2+3=52+3=5) incorrectly. Choice C is incorrect because it forgets to divide by 5. Choice D is incorrect because it divides 60 by 12 or similar error.