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Solve the equation
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Graph
$y = - \dfrac { 2 } { 3 } x$
$y = \dfrac { 1 } { 2 } x + 5$
$x$Intercept
$\left ( 0 , 0 \right )$
$y$Intercept
$\left ( 0 , 0 \right )$
$x$Intercept
$\left ( - 10 , 0 \right )$
$y$Intercept
$\left ( 0 , 5 \right )$
$- \dfrac{ 2 }{ 3 } x = \dfrac{ 1 }{ 2 } x+5$
$x = - \dfrac { 30 } { 7 }$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 } { 3 } } \color{#FF6800}{ x } = \dfrac { 1 } { 2 } x + 5$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 x } { 3 } } = \dfrac { 1 } { 2 } x + 5$
$- \dfrac { 2 x } { 3 } = \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } + 5$
$ $ Calculate the multiplication expression $ $
$- \dfrac { 2 x } { 3 } = \color{#FF6800}{ \dfrac { x } { 2 } } + 5$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 x } { 3 } } = \color{#FF6800}{ \dfrac { x } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) \right ) = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 30 }$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) \right ) = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 30 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = \color{#FF6800}{ 30 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 30$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } = 30$
$\color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ 30 }$
$ $ Change the sign of both sides of the equation $ $
$7 x = - 30$
$\color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 30 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 30 } { 7 } }$
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