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Solve the equation
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Graph
$y = 2 x - \dfrac { 11 x + 19 } { 4 }$
$y = - \dfrac { 19 + 2 x } { 9 }$
$x$Intercept
$\left ( - \dfrac { 19 } { 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 19 } { 4 } \right )$
$x$Intercept
$\left ( - \dfrac { 19 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 19 } { 9 } \right )$
$2x- \dfrac{ 11x+19 }{ 4 } = - \dfrac{ 19+2x }{ 9 }$
$x = - 5$
$ $ Solve a solution to $ x$
$2 x - \dfrac { 11 x + 19 } { 4 } = - \dfrac { \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } } { 9 }$
$ $ Organize the expression $ $
$2 x - \dfrac { 11 x + 19 } { 4 } = - \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 19 } } { 9 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 x + 19 } { 4 } } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 x + 19 } { 9 } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 72 } \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 9 } \left ( \color{#FF6800}{ 11 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 19 } \right ) \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 76 }$
$\color{#FF6800}{ 72 } \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 9 } \left ( \color{#FF6800}{ 11 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 19 } \right ) \right ) = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 76 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 76 } \color{#FF6800}{ + } \color{#FF6800}{ 171 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ x } = - 76 + 171$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 19 } \color{#FF6800}{ x } = - 76 + 171$
$\color{#FF6800}{ - } \color{#FF6800}{ 19 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 76 } \color{#FF6800}{ + } \color{#FF6800}{ 171 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ 19 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 95 }$
$\color{#FF6800}{ 19 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 95 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$x = - 5$
Solve the fractional equation
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 x + 19 } { 4 } } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 19 + 2 x } { 9 } }$
$ $ Reverse the left and right terms of the equation (or inequality) $ $
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 19 + 2 x } { 9 } } = \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 x + 19 } { 4 } }$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 19 + 2 x } { 9 } } = \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 x + 19 } { 4 } }$
$ $ If $ -\frac{a(x)}{b(x)} = c(x) $ is valid, it is $ \begin{cases} -a(x) = b(x) c(x) \\ b(x) \ne 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \left ( \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) = \color{#FF6800}{ 9 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 x + 19 } { 4 } } \right ) \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \left ( \color{#FF6800}{ 19 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) = \color{#FF6800}{ 9 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 11 x + 19 } { 4 } } \right ) \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Simplify the expression $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 19 } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 27 x + 171 } { 4 } } \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 19 } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 27 x + 171 } { 4 } } \\ 9 \neq 0 \end{cases}$
$ $ Reverse the left and right terms of the equation (or inequality) $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 27 x + 171 } { 4 } } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 19 } \\ 9 \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 27 x + 171 } { 4 } } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 19 } \\ 9 \neq 0 \end{cases}$
$ $ If $ -\frac{a(x)}{b(x)} = c(x) $ is valid, it is $ \begin{cases} -a(x) = b(x) c(x) \\ b(x) \ne 0 \end{cases}$
$\begin{cases} \begin{cases} \color{#FF6800}{ - } \left ( \color{#FF6800}{ 27 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 171 } \right ) = \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 19 } \right ) \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases} \\ 9 \neq 0 \end{cases}$
$\begin{cases} \begin{cases} \color{#FF6800}{ - } \left ( \color{#FF6800}{ 27 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 171 } \right ) = \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 19 } \right ) \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases} \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ If there is a system of equations (inequality) in the system of equations (inequality), take it out. $ $
$\begin{cases} \color{#FF6800}{ - } \left ( \color{#FF6800}{ 27 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 171 } \right ) = \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 19 } \right ) \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \left ( \color{#FF6800}{ 27 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 171 } \right ) = \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 19 } \right ) \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Simplify the expression $ $
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 171 } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 76 } \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 171 } = \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 76 } \\ 4 \neq 0 \\ 9 \neq 0 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ 4 \neq 0 \\ 9 \neq 0 \end{cases}$
$\begin{cases} x = - 5 \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \\ 9 \neq 0 \end{cases}$
$ $ There are infinitely many solutions if both sides of $ \ne $ are different. $ $
$\begin{cases} x = - 5 \\ \text{해가 무수히 많습니다} \\ 9 \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \text{해가 무수히 많습니다} \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Ignore the cases where the system of equations where there are infinitely many solutions. $ $
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = - 5 \\ \color{#FF6800}{ 9 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ There are infinitely many solutions if both sides of $ \ne $ are different. $ $
$\begin{cases} x = - 5 \\ \text{해가 무수히 많습니다} \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \text{해가 무수히 많습니다} \end{cases}$
$ $ Ignore the cases where the system of equations where there are infinitely many solutions. $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
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