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Solve the equation
Answer
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Graph
$y = \dfrac { x - 1 } { 2 }$
$y = \dfrac { x + 2 } { 3 }$
$x$Intercept
$\left ( 1 , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 1 } { 2 } \right )$
$x$Intercept
$\left ( - 2 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 2 } { 3 } \right )$
$\dfrac{ x-1 }{ 2 } = \dfrac{ x+2 }{ 3 }$
$x = 7$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ \dfrac { x - 1 } { 2 } } = \color{#FF6800}{ \dfrac { x + 2 } { 3 } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 3 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ 3 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = 2 x + 4$
$ $ Multiply each term in parentheses by $ 3$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } = 2 x + 4$
$3 x - 3 = \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 4$
$ $ Move the variable to the left-hand side and change the symbol $ $
$3 x - 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } = 4$
$\color{#FF6800}{ 3 } x \color{#FF6800}{ - } \color{#FF6800}{ 3 } - 2 x = 4$
$ $ Move the constant to the right side and change the sign $ $
$3 x - 2 x = 4 \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } = 4 + 3$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = 4 + 3$
$x = \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$ $ Add $ 4 $ and $ 3$
$x = \color{#FF6800}{ 7 }$
$x = 7$
Solve the fractional equation
$\color{#FF6800}{ \dfrac { x - 1 } { 2 } } = \color{#FF6800}{ \dfrac { x + 2 } { 3 } }$
$ $ If $ \frac{a(x)}{b(x)} = \frac{c(x)}{d(x)} $ is valid, it is $ \begin{cases} a(x) d(x) = b(x) c(x) \\ b(x) \ne 0 \\ d(x) \ne 0 \end{cases}$
$\begin{cases} \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Simplify the expression $ $
$\begin{cases} \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \\ 2 \neq 0 \\ 3 \neq 0 \end{cases}$
$ $ Solve a solution to $ x$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 7 } \\ 2 \neq 0 \\ 3 \neq 0 \end{cases}$
$\begin{cases} x = 7 \\ \color{#FF6800}{ 2 } \neq \color{#FF6800}{ 0 } \\ 3 \neq 0 \end{cases}$
$ $ There are infinitely many solutions if both sides of $ \ne $ are different. $ $
$\begin{cases} x = 7 \\ \text{해가 무수히 많습니다} \\ 3 \neq 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 7 } \\ \text{해가 무수히 많습니다} \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ Ignore the cases where the system of equations where there are infinitely many solutions. $ $
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 7 } \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} x = 7 \\ \color{#FF6800}{ 3 } \neq \color{#FF6800}{ 0 } \end{cases}$
$ $ There are infinitely many solutions if both sides of $ \ne $ are different. $ $
$\begin{cases} x = 7 \\ \text{해가 무수히 많습니다} \end{cases}$
$\begin{cases} \color{#FF6800}{ x } = \color{#FF6800}{ 7 } \\ \text{해가 무수히 많습니다} \end{cases}$
$ $ Ignore the cases where the system of equations where there are infinitely many solutions. $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 7 }$
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