Write an absolute value inequality that represents the verbal statement, The set of all real numbers x for which the distance from 0 to $8$ less than three times x is more than $2$ .

A) $∣3 x - 8∣ > 2$
B) $∣3 x - 2∣ < 8$
C) $\leq 8$
D) $∣3 x + 8∣ < 2$
E) $\leq 2$

Question

Write an absolute value inequality that represents the verbal statement, The set of all real numbers x for which the distance from 0 to 8 8 8 less than three times x is more than 2 2 2 .A) 2> ∣ 3 x − 8 ∣ > 2 | 3 x - 8 | > 2 ∣3 x − 8∣ > 2 B) ∣ 3 x − 2 ∣ < 8 | 3 x - 2 | < 8 ∣3 x − 2∣ < 8 C) ∣ 3 x + 2 ∣ ≤ 8 | 3 x + 2 | \leq 8 ∣3 x + 2∣ ≤ 8 D) ∣ 3 x + 8 ∣ < 2 | 3 x + 8 | < 2 ∣3 x + 8∣ < 2 E) ∣ 3 x − 8 ∣ ≤ 2 | 3 x - 8 | \leq 2 ∣3 x − 8∣ ≤ 2

David Greenfield · Accepted Answer

Final Answer : A, Explanation : The inequality should represent the distance from 0 to 8 (which is 8) being less than three times x and more than 2, so we can write it as: 2> ∣ 8 − 3 x ∣ > 2 |8-3x| > 2 ∣8 − 3 x ∣ > 2 Which simplifies to: 8-3x ext{ or }8-3x>2> − 2 > 8 − 3 x or 8 − 3 x > 2 -2 > 8-3x ext{ or }8-3x > 2 − 2 > 8 − 3 x or 8 − 3 x > 2 Solving these inequalities gives: \frac{10}{3} ext{ or }x <\frac{2}{3}> x > 10 3 or x < 2 3 x > \frac{10}{3} ext{ or }x < \frac{2}{3} x > 3 10 or x < 3 2 So the correct inequality is: 2}> ∣ 3 x − 8 ∣ > 2 \boxed{|3x-8| > 2} ∣3 x − 8∣ > 2

Write an absolute value inequality that represents the verbal statement, The set of all real numbers x for which the distance from 0 to $8$ less than three times x is more than $2$ .

A) $∣3 x - 8∣ > 2$
B) $∣3 x - 2∣ < 8$
C) $\leq 8$
D) $∣3 x + 8∣ < 2$
E) $\leq 2$

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