To find the distance between the numbers [tex]\(-10.5\)[/tex] and [tex]\(7\)[/tex] on a number line, you can use the absolute difference formula. The absolute difference gives the non-negative difference between two numbers.
The formula to compute the distance [tex]\(d\)[/tex] between two numbers [tex]\(a\)[/tex] and [tex]\(b\)[/tex] is:
[tex]\[
d = |a - b|
\][/tex]
Here, [tex]\(a = -10.5\)[/tex] and [tex]\(b = 7\)[/tex].
Step-by-step solution:
1. Subtract [tex]\(b\)[/tex] from [tex]\(a\)[/tex]:
[tex]\[
a - b = -10.5 - 7
\][/tex]
2. Perform the subtraction:
[tex]\[
-10.5 - 7 = -17.5
\][/tex]
3. Take the absolute value of the result to get the distance:
[tex]\[
d = |-17.5| = 17.5
\][/tex]
Therefore, the distance between [tex]\(-10.5\)[/tex] and [tex]\(7\)[/tex] on a number line is [tex]\(17.5\)[/tex]. The final result is:
[tex]\[
(-10.5, 7, 17.5)
\][/tex]
This means the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and the distance [tex]\(d\)[/tex] are:
[tex]\[
a = -10.5, \quad b = 7, \quad d = 17.5
\][/tex]
