Given the inequalities $7m \ge 3n - 14$ and $|n| \le 5$, which of the following CANNOT be the value of $m$?

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Given the inequalities 7 m \geq 3 n - 14 and ∣ n ∣ \leq 5, which of the following CANNOT be the value of m ?

Explanation	Calculations	Help
$We turn the absolute value condition on n into a range for n .$	$∣ n ∣ \leq 5 - 5 \leq n n \leq 5$	Theory & Tactics Method Card INEQ3 Click to view full details
$We isolate m by dividing the inequality 7 m \geq 3 n - 14 by the positive number 7.$	$7 m \geq 3 n - 14 m \geq \frac{3 n - 14}{7}$	Theory & Tactics Method Card INEQ1-A Click to view full details
$We find the lowest bound for m by using the smallest n = - 5 .$	$m \geq \frac{3 \times ( - 5 ) - 14}{7} m \geq \frac{- 29}{7} \approx - 4.14$
$We compare this bound to each choice and see that -5 is less than about -4.14.$	$- 5 < \frac{- 29}{7} \approx - 4.14$

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A

Given the inequalities 7 m \geq 3 n - 14 and ∣ n ∣ \leq 5, which of the following CANNOT be the value of m ?

Explanation	Calculations	Help
$We turn the absolute value condition on n into a range for n .$	$∣ n ∣ \leq 5 - 5 \leq n n \leq 5$	Theory & Tactics Method Card INEQ3 Click to view full details
$We isolate m by dividing the inequality 7 m \geq 3 n - 14 by the positive number 7.$	$7 m \geq 3 n - 14 m \geq \frac{3 n - 14}{7}$	Theory & Tactics Method Card INEQ1-A Click to view full details
$We find the lowest bound for m by using the smallest n = - 5 .$	$m \geq \frac{3 \times ( - 5 ) - 14}{7} m \geq \frac{- 29}{7} \approx - 4.14$
$We compare this bound to each choice and see that -5 is less than about -4.14.$	$- 5 < \frac{- 29}{7} \approx - 4.14$

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A