9

Set 17: Linear Inequalities

Explanation

Answer: A

If 83x2x+38- 3x \geq 2x + 3, what is the solution?

A.

x1x \leq 1

✓ Correct
B.

x1x \geq 1

C.

x5x \leq 5

D.

x5x \geq 5

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Variables on both sides require systematic collection. 1. Subtract 2 x: 83x2x38- 3 x - 2 x \geq 3, giving 85x38- 5 x \geq 3 2. Subtract 8: 5x5-5 x \geq -5 3. Divide by -5: x1x \leq 1 (REVERSE!) Strategic Tip: Collect all variable terms on one side first, then isolate the variable. Choice B is incorrect because it fails to reverse when dividing by -5. Choice C is incorrect because it might come from adding 8 and 3 instead of proper solving. Choice D is incorrect because it combines wrong value and wrong direction.

Key Steps:

The correct answer is x1x \leq 1

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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