Answer :
Certainly! Let's find the distance between the numbers [tex]\(-172\)[/tex] and [tex]\(-69\)[/tex] on the number line step by step:
1. Identify the two points:
- The first point is [tex]\(-172\)[/tex].
- The second point is [tex]\(-69\)[/tex].
2. Understand what distance means:
- The distance between any two points on a number line is the absolute value of the difference between these two points.
3. Calculate the difference between the points:
[tex]\[
-172 - (-69) = -172 + 69
\][/tex]
- Here, subtracting a negative number is the same as adding the positive equivalent.
[tex]\[
-172 + 69 = -103
\][/tex]
4. Take the absolute value:
- The absolute value of [tex]\(-103\)[/tex] is [tex]\(\| -103 \| = 103\)[/tex].
5. Conclusion:
- The distance between [tex]\(-172\)[/tex] and [tex]\(-69\)[/tex] on the number line is [tex]\(103\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{103}
\][/tex]
1. Identify the two points:
- The first point is [tex]\(-172\)[/tex].
- The second point is [tex]\(-69\)[/tex].
2. Understand what distance means:
- The distance between any two points on a number line is the absolute value of the difference between these two points.
3. Calculate the difference between the points:
[tex]\[
-172 - (-69) = -172 + 69
\][/tex]
- Here, subtracting a negative number is the same as adding the positive equivalent.
[tex]\[
-172 + 69 = -103
\][/tex]
4. Take the absolute value:
- The absolute value of [tex]\(-103\)[/tex] is [tex]\(\| -103 \| = 103\)[/tex].
5. Conclusion:
- The distance between [tex]\(-172\)[/tex] and [tex]\(-69\)[/tex] on the number line is [tex]\(103\)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{103}
\][/tex]
