8

Set 5: Linear Inequalities

Explanation

Answer: A

Which inequality represents the region between y=xy=x and y=x+2y=x+2?

A.

x<y<x+2x < y < x + 2

✓ Correct
B.

x>y>x+2x > y > x + 2

C.

y<xy < x or y>x+2y > x + 2

D.

y>xy > x and y>x+2y > x + 2

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Band between parallel lines. 1. Above y=xy=x: y>xy > x (or x<yx < y) 2. Below y=x+2y=x+2: y<x+2y < x + 2 3. Combine: x<y<x+2x < y < x + 2 Strategic Tip: Verify that x<x+2x < x+2 is true (it is), so the inequality makes sense. Choice B is incorrect because x>x+2x > x+2 is impossible. Choice C is incorrect because it is outside the band. Choice D is incorrect because it is above both lines.

Key Steps:

The correct answer is x<y<x+2x < y < x + 2

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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