SOLUTION: what is the distance between -8 and -1 on the number line and -3 and 6?

Algebra ->  Number-Line -> SOLUTION: what is the distance between -8 and -1 on the number line and -3 and 6?      Log On


   

Question 1052142: what is the distance between -8 and -1 on the number line and -3 and 6?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
what is the distance between -8 and -1 on the number line and -3 and 6?
~~~~~~~~~~~~~~~~~~~~~`

The distance between -8 and -1 on the number line is |(-8) - (-1)| = |-8 + 1| = |-7| = 7.


The distance between -3 and 6 on the number line is |(-3) - 6| = |-3 - 6| = |-9| = 9.


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the distance between -8 and -1 would be equal to the absolute value of -1 - (-8) or the absolute value of -8 - (-1).

-1 - (-8) is equal to -1 + 8 which is equal to 8 - 1 which is equal to 7.

the absolute value of 7 is equal to 7.

-8 - (-1) is equal to -8 + 1 which is equal to - (8 - 1) which is equal to -7.

the absolute value of -7 is equal to 7.

the distance between -8 and -1 is therefore 7.

you can also draw a number line and count the distance between them as follows:

assume each . is one unit. 



             .     .     .     .     .     .     .     . 
            -8    -7    -6    -5    -4    -3    -2    -1
             .----->----->----->----->----->----->----->
             <-----<-----<-----<-----<-----<-----<-----.


starting form -8, it takes you 7 dots to get to -1.

starting from -1, it takes you 7 dots to get to -8.

the distance between them is therefore 7 dots which means the distance between them is 7 units.



the distance between -3 and 6 would be the absolute value of -3 - 6 or the absolute value of 6 - (-3).

-3 - 6 is equal to -9.

the absolute value of -9 is equal to 9.

6 - (-3) is equal to 6 + 3 which is equal to 9.

the absolute value of 9 is equal to 9.

the distance between -3 and 6 is therefore equal to 9.

you can also draw the number lines as we did before and count the number of units to get from -3 to 6 as shown below:

each unit is represented by a dot (dot = .). 



             .     .     .     .     .     .     .     .     .     . 
            -3    -2    -1     0     1     2     3     4     5     6
             .----->----->----->----->----->----->----->----->----->
             <-----<-----<-----<-----<-----<-----<-----<-----<-----.


starting from -3, it takes you 9 dots to get to 6.

starting from 6, it takes you 9 dots to get to -3.

the distance between them is therefore 9 dots which means the distance between them is 9 units.

the absolute value of any numbers is always positive.

if the number is negative, you just reverse the sign to make it positive.

if the number is positive, you just leave it as is because it's already positive.