The distance between two numbers on the number line is 9. If one of the numbers is 7, what are the two possibilities for the other number?

To find the two possible values for the other number, given that the distance between the two numbers is 9 and one of the numbers is 7, you can set up the following equation:

\[
|x - 7| = 9
\]

This equation represents the absolute difference between the two numbers. We can solve it by considering the two possible cases:

### Case 1: Positive Distance
\[
x - 7 = 9
\]
\[
x = 9 + 7 = 16
\]

### Case 2: Negative Distance
\[
x - 7 = -9
\]
\[
x = -9 + 7 = -2
\]

### Conclusion:
The two possibilities for the other number are **16** and **-2**.

Do you have any questions or need further details? Here are some related questions you might find interesting:

1. How do you calculate the distance between two points on a coordinate plane?
2. What is the distance between 10 and -4 on the number line?
3. How can you determine the midpoint between two numbers on a number line?
4. How does the concept of absolute value relate to distance on the number line?
5. What is the distance between -7 and 2 on the number line?

**Tip:** When solving problems involving distance on the number line, remember to consider both the positive and negative cases in the absolute value equation.

Explore how to calculate the distance between two numbers on a number line with a step-by-step solution. Given that the distance is 9 and one number is 7, find the two possible values for the other number. Learn about absolute value and its application in solving distance problems on the number line. Suitable for students in Grades 6-8.

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