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Math Help - solve absolute value

  1. #1
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    solve absolute value

    |2x-3/9|=5
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  2. #2
    MHF Contributor arbolis's Avatar
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    |2x-3/9|=5 Is equivalent to say that -5<2x-\frac{3}{9}<5, or -5+\frac{3}{9}<2x<5+\frac{3}{9}, or \frac{{-5}+{\frac{3}{9}}}{2}<x<\frac{{5}+{\frac{3}{9}}}{2}. Almost done, I let you simplify the fractions.
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  3. #3
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    Hello, super9xman!

    Solve: . \left| \frac{2x-3}{9}\right|\:=\:5

    We have: . \begin{Bmatrix}\dfrac{2x-3}{9}  & = & \text{-}5 \\ \\ \dfrac{2x-3}{9} &=& 5 \end{Bmatrix}<br />
\quad\Rightarrow\quad \begin{Bmatrix}2x-3&=&\text{-}45 \\ \\ 2x-3&=&45 \end{Bmatrix} . \Rightarrow\quad\begin{Bmatrix}2x &=&\text{-}42 \\ \\ 2x &=&48 \end{Bmatrix}\quad\Rightarrow\quad \begin{Bmatrix}x &=&\text{-}21 \\ \\ x&=& 24\end{Bmatrix}

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