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

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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

Answers

Answer: [tex]6.7<x<9.7[/tex].Step-by-step explanation:We have been given an inequality [tex]|x-8.2|-1.5<0[/tex] and we are asked to solve our given inequality.Let us add 1.5 to both sides of our inequality.[tex]|x-8.2|-1.5+1.5<0+1.5[/tex][tex]|x-8.2|<0+1.5[/tex]Upon using definition of absolute value function [tex]|f(x)|<a\Rightarrow f(x)<a \text{ and } f(x)>-a[/tex] we can write our absolute function as:[tex]x-8.2<1.5\text{ and } x-8.2>-1.5[/tex]   [tex]x<1.5+8.2\text{ and } x>-1.5+8.2[/tex]  [tex]x<9.7\text{ and } x>6.7[/tex]  Upon combining our ranges we will get,[tex]6.7<x<9.7[/tex]  Therefore, our inequality solves to [tex]6.7<x<9.7[/tex].

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