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Solve the equation
Answer
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Graph
$y = \dfrac { 1 } { 3 } x + \dfrac { 1 } { 2 }$
$y = \dfrac { 1 } { 2 } x + \dfrac { 2 } { 3 }$
$x$Intercept
$\left ( - \dfrac { 3 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 1 } { 2 } \right )$
$x$Intercept
$\left ( - \dfrac { 4 } { 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 2 } { 3 } \right )$
$\dfrac{ 1 }{ 3 } x+ \dfrac{ 1 }{ 2 } = \dfrac{ 1 }{ 2 } x+ \dfrac{ 2 }{ 3 }$
$x = - 1$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ \dfrac { 1 } { 3 } } \color{#FF6800}{ x } + \dfrac { 1 } { 2 } = \dfrac { 1 } { 2 } x + \dfrac { 2 } { 3 }$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { x } { 3 } } + \dfrac { 1 } { 2 } = \dfrac { 1 } { 2 } x + \dfrac { 2 } { 3 }$
$\dfrac { x } { 3 } + \dfrac { 1 } { 2 } = \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } + \dfrac { 2 } { 3 }$
$ $ Calculate the multiplication expression $ $
$\dfrac { x } { 3 } + \dfrac { 1 } { 2 } = \color{#FF6800}{ \dfrac { x } { 2 } } + \dfrac { 2 } { 3 }$
$\color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 2 } } = \color{#FF6800}{ \dfrac { x } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 2 } { 3 } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$2 x + 3 = \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 4$
$ $ Move the variable to the left-hand side and change the symbol $ $
$2 x + 3 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 4$
$2 x \color{#FF6800}{ + } \color{#FF6800}{ 3 } - 3 x = 4$
$ $ Move the constant to the right side and change the sign $ $
$2 x - 3 x = 4 \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 4 - 3$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ x } = 4 - 3$
$- x = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Subtract $ 3 $ from $ 4$
$- x = \color{#FF6800}{ 1 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ 1 }$
$ $ Change the sign of both sides of the equation $ $
$x = - 1$
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