Set 8: Linear Inequalities

Explanation

Answer: A

A gym charges a $ $50initiation fee and \$ 30 per month. A competitor charges no initiation fee but $40 per month. After how many months $$m$ is the competitor's gym more expensive?

$m > 5$

✓ Correct

$m < 5$

$m > 2$

$m < 2$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Compare the total costs of both gyms. 1. Gym 1 Cost: $50+ 30 m$ 2. Gym 2 Cost: $40m$ 3. Condition: Gym 2 > Gym 1 4. Inequality: $40m > 50 + 30 m$ 5. Subtract 30 m: $10m > 50$ 6. Divide by 10: $m > 5$ Strategic Tip: Set up an expression for each option and use the inequality symbol that matches the question ("more expensive" = $>$ ). Choice B is incorrect because it reverses the direction ( $m < 5$ ), implying the competitor is cheaper after 5 months. Choice C is incorrect because it uses the wrong value. Choice D is incorrect because it combines wrong value and wrong direction.

Key Steps:

•

The correct answer is $m > 5$

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 8: Linear Inequalities

Detailed Explanation

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