Set 17: Linear Inequalities (Advanced)

Choice A is correct. 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: $6(\frac{x}{2}) + 6(\frac{x}{3}) > 6(10)$ 3. Simplify: $3x + 2 x > 60$ 4. Combine: $5x > 60$ 5. Divide by 5: $x > 12$ Strategic Tip: Alternatively, $\frac{x}{2} + \frac{x}{3} = \frac{3 x}{6} + \frac{2 x}{6} = \frac{5 x}{6}$. Then $\frac{5 x}{6} > 10 \rightarrow 5 x > 60 \rightarrow x > 12$. Choice B is incorrect because it might come from adding denominators ($2 +3=5$) 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.