9

Set 4: Linear Equations (Intermediate)

Explanation

Answer: B

If 3x+2y=123x + 2y = 12 and yy is positive, what is the maximum integer value for xx?

A.

5

B.

3

✓ Correct
C.

4

D.

2

Detailed Explanation

Choice B is correct. Choice C is the correct answer. 1. Solve for y: 2y=123xy=61.5x2y = 12 - 3 x \rightarrow y = 6 - 1.5 x 2. Condition: y>061.5x>0y > 0 \rightarrow 6 - 1.5 x > 0 3. Solve: 6>1.5x4>x6> 1.5 x \rightarrow 4 > x 4. Max Integer: Since x<4x < 4, max integer is 3. Choice A is incorrect because if x=4, y=0 (not positive). Choice C is incorrect because 2 is valid but not max. Choice D is incorrect because 5 makes y negative.

Key Steps:

The correct answer is 3

Why others are wrong:
A: Choice A 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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