Question

Use absolute value to express the distance between −10 and 16 on the number line.

Answer 1

Explanation:

There are several things you need to know in order to write the absolute value equation for a situation. First is how to formulate what you need. The absolute value equation follows the formatting:

| x - midpoint | = the distance between the midpoint and one of the endpoints.

That means we also need to be able to find the midpoint of -10 and 16. Finding the midpoint is finding the middle, which is the same as finding an average of the 2 numbers.

`M=(-10+16)/(2)=3`

So the midpoint is 3. The distance between 3 and either one of the endpoints is going to be the same, by definition of the midpoint of the 2 numbers. The distance between 3 and 16 is 13 units. The distance between 3 and -10 is also 13 units. So, to put this into an absolute value equation,

| x - 3 | = 13

Answer 2

Answer: 26

Explanation:

From -10 to 0 will be 10

1 to 16 are 16