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uysha [10]
2 years ago
10

Look at the picture​

Mathematics
1 answer:
Sonbull [250]2 years ago
6 0

\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{$\begin{gathered}\sf  \frac{9(|x-8|)}{9} < \frac{36}{9}   \end{gathered}$}
  • \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{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}

<u>                                                                                                                             </u>

         \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{$\begin{gathered}\sf x < 12 \end{gathered}$}

<u>                                                                                                                             </u>

           \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{$\begin{gathered}\sf x > 4 \end{gathered}$}

<u>                                                                                                                             </u>

<u />\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{$\begin{gathered}\sf is \ \bf{\underline{"A"}}. \end{gathered}$}

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