Question

Look at the picture​

Answer 1

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

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

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

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

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

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

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

                                                                                                                           

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

                                                                                                                           

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

                                                                                                                           

$\underline{\boldsymbol{\sf{Answer}}}$

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

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