Question

Dr. Jones has found over the years that 95% of babies delivered weighted x pounds, where |x-8.2| - 1.5 < 0.....Solve the inequality....Show work

Answer 1

`6.7<x<9.7`.

Explanation:

We have been given an inequality
`|x-8.2|-1.5<0` and we are asked to solve our given inequality.

Let us add 1.5 to both sides of our inequality.

`|x-8.2|-1.5+1.5<0+1.5`

`|x-8.2|<0+1.5`

Upon using definition of absolute value function
`|f(x)|<a\Rightarrow f(x)<a \text{ and } f(x)>-a` we can write our absolute function as:

`x-8.2<1.5\text{ and } x-8.2>-1.5`

`x<1.5+8.2\text{ and } x>-1.5+8.2`

`x<9.7\text{ and } x>6.7`

Upon combining our ranges we will get,

`6.7<x<9.7`

Therefore, our inequality solves to
`6.7<x<9.7`.