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Solve the equation
Answer
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Graph
$y = \dfrac { x } { 3 } - \dfrac { 1 } { 2 }$
$y = \dfrac { x } { 4 }$
$x$Intercept
$\left ( \dfrac { 3 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 1 } { 2 } \right )$
$x$Intercept
$\left ( 0 , 0 \right )$
$y$Intercept
$\left ( 0 , 0 \right )$
$\dfrac{ x }{ 3 } - \dfrac{ 1 }{ 2 } = \dfrac{ x }{ 4 }$
$x = 6$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } = \color{#FF6800}{ \dfrac { x } { 4 } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } = \color{#FF6800}{ 3 } \color{#FF6800}{ x }$
$4 x - 6 = \color{#FF6800}{ 3 } \color{#FF6800}{ x }$
$ $ Move the variable to the left-hand side and change the symbol $ $
$4 x - 6 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 0$
$4 x \color{#FF6800}{ - } \color{#FF6800}{ 6 } - 3 x = 0$
$ $ Move the constant to the right side and change the sign $ $
$4 x - 3 x = \color{#FF6800}{ 6 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 6$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = 6$
$x = 6$
Solve the fractional equation
$\color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } = \color{#FF6800}{ \dfrac { x } { 4 } }$
$ $ Reverse the left and right terms of the equation (or inequality) $ $
$\color{#FF6800}{ \dfrac { x } { 4 } } = \color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
$\color{#FF6800}{ \dfrac { x } { 4 } } = \color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
$ $ 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}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \right ) \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \right ) \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Simplify the expression $ $
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 4 x - 6 } { 3 } } \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 4 x - 6 } { 3 } } \\ 4 \neq 0 \end{cases}$
$ $ Reverse the left and right terms of the equation (or inequality) $ $
$\begin{cases} \color{#FF6800}{ \dfrac { 4 x - 6 } { 3 } } = \color{#FF6800}{ x } \\ 4 \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ \dfrac { 4 x - 6 } { 3 } } = \color{#FF6800}{ x } \\ 4 \neq 0 \end{cases}$
$ $ 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}$
$\begin{cases} \begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \end{cases} \\ 4 \neq 0 \end{cases}$
$\begin{cases} \begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \end{cases} \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ If there is a system of equations (inequality) in the system of equations (inequality), take it out. $ $
$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \\ 3 \neq 0 \\ 4 \neq 0 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 6 } \\ 3 \neq 0 \\ 4 \neq 0 \end{cases}$
$\begin{cases} x = 6 \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \\ 4 \neq 0 \end{cases}$
$ $ There are infinitely many solutions if both sides of $ \ne $ are different. $ $
$\begin{cases} x = 6 \\ \text{해가 무수히 많습니다} \\ 4 \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 6 } \\ \text{해가 무수히 많습니다} \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Ignore the cases where the system of equations where there are infinitely many solutions. $ $
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 6 } \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = 6 \\ \color{#FF6800}{ 4 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ There are infinitely many solutions if both sides of $ \ne $ are different. $ $
$\begin{cases} x = 6 \\ \text{해가 무수히 많습니다} \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 6 } \\ \text{해가 무수히 많습니다} \end{cases}$
$ $ Ignore the cases where the system of equations where there are infinitely many solutions. $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 6 }$
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