4

Set 17: Linear Inequalities

Explanation

Answer: A

Which point is NOT a solution to y3x1y \geq 3x - 1?

A.

(0,2)(0, -2)

✓ Correct
B.

(1,2)(1, 2)

C.

(2,6)(2, 6)

D.

(0,0)(0, 0)

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Test each point. We want the one that makes the inequality FALSE. 1. Test (0, -2): 23(0)121-2 \geq 3(0) - 1 \rightarrow -2 \geq -1. This is FALSE. (-2 is smaller than -1). So this is the answer. 2. Test (1, 2): 23(1)1222\geq 3(1) - 1 \rightarrow 2 \geq 2. True. 3. Test (2, 6): 63(2)1656\geq 3(2) - 1 \rightarrow 6 \geq 5. True. 4. Test (0, 0): 03(0)1010\geq 3(0) - 1 \rightarrow 0 \geq -1. True. Strategic Tip: Always watch for "NOT" in the question stem. Choice B is incorrect because it is a solution. Choice C is incorrect because it is a solution. Choice D is incorrect because it is a solution.

Key Steps:

The correct answer is (0,2)(0, -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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