Final answer:
The compound inequality x - 7 < -9 or x - 7 > 9 is equivalent to the absolute value inequality |x - 7| > 9.
Step-by-step explanation:
The compound inequality given is x − 7 < − 9 or x − 7 > 9. To rewrite this compound inequality as an absolute value inequality, we recognize that we're dealing with distances from the point 7 on the number line. We want to find when x is either more than 9 units to the right or more than 9 units to the left of 7. This is equivalent to saying that the absolute value of x − 7 is greater than 9. So, the absolute value inequality is |x − 7| > 9.