Set 16: Linear Inequalities (Advanced)

Explanation

Answer: A

Which compound inequality has NO solution?

$x < 3$ and $x > 5$

✓ Correct

$x < 3$ or $x > 5$

$x > 3$ and $x < 5$

$x > 3$ or $x < 5$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Analyze the logic of "and". 1. Condition: A number must be less than 3 AND greater than 5 simultaneously. 2. Logic: No number exists that satisfies both. The sets are disjoint. 3. Result: Empty set (No solution). Strategic Tip: "And" requires overlap. If the arrows point away from each other with a gap, there is no overlap. Choice B is incorrect because "Or" allows disjoint sets (this is a valid inequality). Choice C is incorrect because numbers like 4 satisfy this ( $3< x < 5$ ). Choice D is incorrect because this covers all real numbers (overlapping rays).

Key Steps:

•

The correct answer is $x < 3$ and $x > 5$

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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Set 16: Linear Inequalities (Advanced)

Detailed Explanation

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