10

Set 10: Linear Inequalities

Explanation

Answer: A

Solve: 2(3x1)4x102(3x - 1) - 4x \leq 10

A.

x6x \leq 6

✓ Correct
B.

x6x \geq 6

C.

x4x \leq 4

D.

x4x \geq 4

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Simplify the expression on the left side first. 1. Distribute: 6x24x106x - 2 - 4 x \leq 10 2. Combine like terms: 2x2102x - 2 \leq 10 3. Add 2: 2x122x \leq 12 4. Divide by 2: x6x \leq 6 Strategic Tip: Combine 6x6x and 4x-4 x carefully to get 2x2x. Choice B is incorrect because it reverses the inequality direction without justification. Choice C is incorrect because it might result from adding 2 to 10 incorrectly (getting 8) or dividing wrong. Choice D is incorrect because it combines wrong value and wrong direction.

Key Steps:

The correct answer is x6x \leq 6

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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