9

Set 11: Linear Inequalities (Advanced)

Explanation

Answer: A

Which inequality describes the region below the dashed line y=3x+4y = -3x + 4?

A.

y<3x+4y < -3x + 4

✓ Correct
B.

y3x+4y \leq -3x + 4

C.

y>3x+4y > -3x + 4

D.

y3x+4y \geq -3x + 4

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Match the line type and shading direction. 1. Dashed line: Indicates strict inequality (<< or >>), not inclusive. 2. Below: Indicates "less than" (y<...y < ...). 3. Combine: y<3x+4y < -3 x + 4 Strategic Tip: Dashed = Strict (<,><, >). Solid = Inclusive (,\leq, \geq). Below = Less. Above = Greater. Choice B is incorrect because \leq requires a solid line. Choice C is incorrect because >> shades above. Choice D is incorrect because \geq shades above and requires a solid line.

Key Steps:

The correct answer is y<3x+4y < -3x + 4

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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