Question

Write the absolute value equation that has the following solution(s). Two solutions: x=2, x=14.

Answer 1

|x-8|=6

Explanation:

i checked rsm its correct :3

Answer 2

`|x-8|=6`

Explanation:

Let's begin by finding the midpoint of 2 and 14. To do this, we'll add the numbers and then divide by 2.

2+14=16

16/2=8

The number that is the same distance between 2 and 14 is 8.

Now, let's find how far away each number is from 8.

8-2=6

14-8=6

2 and 14 are 6 away from 8.

Let's set up the absolute value equation using these two values.

Since 8 is the midpoint, this will be what the absolute value expression is equal to.

Since each number is 6 away from 8, this is the number (6) we will be taking away from 2 and 14.

Remember that absolute value is just distance.

In other words, 2 is 6 away from 8, and 14 is also 6 away from 8.

Or, the distance between a number x and 8 is 6.

Using this knowledge, we have:

`|x-8|=6`