3
algebra

If x4+2<7\frac{x}{4} + 2 < 7, what is the solution?

A

x<20x < 20

B

x>20x > 20

C

x<36x < 36

D

x<9x < 9

Correct Answer: A

Choice A is the correct answer. Inequalities with fractions require careful handling but follow familiar patterns.

  1. Subtract 2: x4+22<72\frac{x}{4} + 2 - 2 < 7 - 2, giving x4<5\frac{x}{4} < 5
  2. Multiply by 4: 4x4<454 \cdot \frac{x}{4} < 4 \cdot 5, giving x<20x < 20
  3. Check: Try x=16x = 16: 164+2=4+2=6<7\frac{16}{4} + 2 = 4 + 2 = 6 < 7 ??n ?�� 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.