Final answer:
The equivalent inequality to the original absolute value inequality |X - 4| < 9 is -9 < X - 4 < 9, which separates the absolute value condition into two parts where X - 4 is greater than -9 and less than 9 simultaneously.
Step-by-step explanation:
The equation |X - 4| < 9 is an absolute value inequality. To solve this, we need to split it into two separate inequalities, without the absolute value. The two cases to consider are when the expression inside the absolute value is positive and when it's negative.
When getting rid of the absolute value, the inequality becomes -9 < X - 4 < 9 because X - 4 must be less than 9 and greater than -9 to satisfy the original inequality. This can also be written as two separate inequalities combined with an and statement: X - 4 > -9 and X - 4 < 9. Therefore, the equivalent inequality that represents the original absolute value inequality is option B: -9 < X - 4 < 9.