Question

Look at the picture
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Answer 1

`\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}`

• 
  `\large\displaystyle\text{$\begin{gathered}\sf (9(|x-8|))/(9) < (36)/(9) \end{gathered}$}`

• 
  `\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}`

• 
  `\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}`

`\underline{\boldsymbol{\sf{Answer}}}`

`\boxed{\large\displaystyle\text{$\begin{gathered}\sf x < 12 \ and \ x > 4 \end{gathered}$} }`

`\large\displaystyle\text{$\begin{gathered}\sf Therefore,\bf{\underline{the \ correct \ option}} \ \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{`