Set 3: Linear Inequalities (Intermediate)

Explanation

Answer: A

Which inequality represents the shaded region below the solid line $y = \frac{1}{2}x - 3$ ?

$y \leq \frac{1}{2}x - 3$

✓ Correct

$y < \frac{1}{2}x - 3$

$y \geq \frac{1}{2}x - 3$

$y > \frac{1}{2}x - 3$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Match line type and shading. 1. Solid line: Inclusive ( $\leq$ or $\geq$ ). 2. Below: Less than ( $\leq$ or $<$ ). 3. Combine: $\leq$ Strategic Tip: "Below" always corresponds to $<$ or $\leq$ . Choice B is incorrect because it implies a dashed line. Choice C is incorrect because it shades above. Choice D is incorrect because it shades above and implies a dashed line.

Key Steps:

•

The correct answer is $y \leq \frac{1}{2}x - 3$

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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