Set 5: Linear Inequalities

Choice C is correct. Choice C is the correct answer. Inequalities with multiple fractions require finding a common denominator. 1. LCD is 4: Rewrite as $\frac{2(6 x-5)}{4} - \frac{3 x+13}{4} > 10$ 2. Combine fractions: $\frac{12 x-10-3 x-13}{4} > 10$, giving $\frac{9 x-23}{4} > 10$ 3. Multiply by 4: $9x - 23 > 40$ 4. Add 23: $9x > 63$ 5. Divide by 9: $x > 7$ Strategic Tip: When working with multiple fractions, find the LCD (Least Common Denominator) to combine fractions efficiently. Choice A is incorrect because it represents $x > 3$, which comes from solving with incorrect arithmetic. Choice B is incorrect because it both uses the wrong value and reverses the inequality direction. Choice D is incorrect because while 7 is the correct boundary, the direction should be $>$, not $<$.