5
algebra

Which inequality represents the region below y=3xy = 3x and above y=3x4y = 3x - 4?

A

3x4<y<3x3x - 4 < y < 3x

B

3x<y<3x43x < y < 3x - 4

C

y<3xy < 3x or y>3x4y > 3x - 4

D

y>3xy > 3x and y<3x4y < 3x - 4

Correct Answer: A

Choice A is the correct answer. Combine the two conditions.

  1. Below y=3xy=3x: y<3xy < 3x
  2. Above y=3x4y=3x-4: y>3x4y > 3x - 4
  3. Combine: 3x4<y<3x3x - 4 < y < 3x

?�� Strategic Tip: This describes a band between two parallel lines.

Choice B is incorrect because it implies 3x<3x43x < 3x - 4, which is impossible (0<40 < -4 is false). Choice C is incorrect because "or" would cover the entire plane (except the lines). Choice D is incorrect because it describes the region above the top line and below the bottom line (empty set).