Set 17: Linear Inequalities

Choice A is correct. Choice A is the correct answer. Inequalities with fractions require careful handling but follow familiar patterns. 1. Subtract 2: $\frac{x}{4} + 2 - 2 < 7 - 2$, giving $\frac{x}{4} < 5$ 2. Multiply by 4: $4\cdot \frac{x}{4} < 4 \cdot 5$, giving $x < 20$ 3. Check: Try $x = 16$: $\frac{16}{4} + 2 = 4 + 2 = 6 < 7$ Strategic Tip: Multiplying both sides by a positive number (like 4) preserves the inequality direction. Choice B is incorrect because it reverses the inequality direction without cause. Choice C is incorrect because it multiplies 7 by 4 first, then adds 8, using incorrect order of operations. Choice D is incorrect because it divides 36 by 4 or uses some other faulty calculation.