8

Set 10: Linear Inequalities (Intermediate)

Explanation

Answer: A

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

A.

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

✓ Correct
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

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Combine the two conditions. 1. Below y=3xy=3 x: y<3xy < 3 x 2. Above y=3x4y=3 x-4: y>3x4y > 3 x - 4 3. Combine: 3x4<y<3x3x - 4 < y < 3 x Strategic Tip: This describes a band between two parallel lines. Choice B is incorrect because it implies 3x<3x43x < 3 x - 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).

Key Steps:

The correct answer is 3x4<y<3x3x - 4 < y < 3x

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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