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 |

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 $8$ less than three times x is more than $2$ .
A) $| 3 x - 8 | > 2$
B) $| 3 x - 2 | < 8$
C) $| 3 x + 2 | \leq 8$
D) $| 3 x + 8 | < 2$
E) $| 3 x - 8 | \leq 2$

Quizplus · Accepted Answer

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:
$$|8-3x|>2$$
Which simplifies to:
$$-2>8-3x	ext{ or }8-3x>2$$
Solving these inequalities gives:
$$x>\frac{10}{3}	ext{ or }x<\frac{2}{3}$$
So the correct inequality is:
$$\boxed{|3x-8|>2}$$

Write an Absolute Value Inequality That Represents the Verbal Statement 888

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