9

Set 4: Linear Inequalities

Explanation

Answer: A

Which point satisfies y<2x+1y < 2x + 1, y>xy > -x, and x<2x < 2?

A.

(1,1)(1, 1)

✓ Correct
B.

(3,0)(3, 0)

C.

(0,1)(0, -1)

D.

(1,4)(1, 4)

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Test (1,1)(1, 1). 1. y<2x+1y < 2 x + 1: 1<2(1)+1=31< 2(1) + 1 = 3 (True) 2. y>xy > -x: 1>11> -1 (True) 3. x<2x < 2: 1<21< 2 (True) 4. Result: All true. Strategic Tip: Check the easiest constraint (x<2x < 2) first to eliminate options. Choice B is incorrect because x=3x=3 fails x<2x < 2. Choice C is incorrect because 1>0-1 > 0 is false (y>xy > -x). Choice D is incorrect because 4<34< 3 is false (y<2x+1y < 2 x + 1).

Key Steps:

The correct answer is (1,1)(1, 1)

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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