Set 9: Linear Inequalities

Explanation

Answer: A

If $\frac{2x - 5}{3} \geq x - 3$ , what is the solution?

$x \leq 4$

✓ Correct

$x \geq 4$

$x \leq 2$

$x \geq 2$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Multiply by the denominator to clear the fraction. 1. Multiply by 3: $2x - 5 \geq 3(x - 3)$ 2. Distribute: $2x - 5 \geq 3 x - 9$ 3. Subtract 2 x: $-5 \geq x - 9$ 4. Add 9: $4\geq x$ , or $x \leq 4$ Strategic Tip: Don't forget to multiply the entire right side $(x-3)$ by 3. Choice B is incorrect because it reverses the inequality direction. Choice C is incorrect because it might result from arithmetic errors. Choice D is incorrect because it combines wrong value and wrong direction.

Key Steps:

•

The correct answer is $x \leq 4$

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 9: Linear Inequalities

Detailed Explanation

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