Set 6: Linear Inequalities (Advanced)

Explanation

Answer: A

Solve: $3x + 4y > 12$ for $y$ .

$y > -\frac{3}{4}x + 3$

✓ Correct

$y < -\frac{3}{4}x + 3$

$y > -\frac{3}{4}x - 3$

$y > \frac{3}{4}x + 3$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Isolate $y$ . 1. Subtract 3 x: $4y > -3 x + 12$ 2. Divide by 4: $y > -\frac{3}{4}x + 3$ Strategic Tip: Dividing by positive 4 keeps the sign direction. Choice B is incorrect because it reverses the sign. Choice C is incorrect because it has wrong intercept sign. Choice D is incorrect because it has wrong slope sign.

Key Steps:

•

The correct answer is $y > -\frac{3}{4}x + 3$

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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