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Solve the equation
Answer
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Graph
$y = \dfrac { 1 } { 3 } x - 2$
$y = - \dfrac { 3 } { 5 } x - 9$
$x$Intercept
$\left ( 6 , 0 \right )$
$y$Intercept
$\left ( 0 , - 2 \right )$
$x$Intercept
$\left ( - 15 , 0 \right )$
$y$Intercept
$\left ( 0 , - 9 \right )$
$x = - \dfrac { 15 } { 2 }$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ x } - 2 = - \dfrac { 3 } { 5 } x - 9$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 3 } } } - 2 = - \dfrac { 3 } { 5 } x - 9$
$\dfrac { x } { 3 } - 2 = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 5 } } } \color{#FF6800}{ x } - 9$
$ $ Calculate the multiplication expression $ $
$\dfrac { x } { 3 } - 2 = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 5 } } } - 9$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 3 } } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 5 } } } \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 30 } = \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 135 }$
$5 x - 30 = \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ x } - 135$
$ $ Move the variable to the left-hand side and change the symbol $ $
$5 x - 30 \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ x } = - 135$
$5 x \color{#FF6800}{ - } \color{#FF6800}{ 30 } + 9 x = - 135$
$ $ Move the constant to the right side and change the sign $ $
$5 x + 9 x = - 135 \color{#FF6800}{ + } \color{#FF6800}{ 30 }$
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ x } = - 135 + 30$
$ $ Organize the expression $ $
$\color{#FF6800}{ 14 } \color{#FF6800}{ x } = - 135 + 30$
$14 x = \color{#FF6800}{ - } \color{#FF6800}{ 135 } \color{#FF6800}{ + } \color{#FF6800}{ 30 }$
$ $ Add $ - 135 $ and $ 30$
$14 x = \color{#FF6800}{ - } \color{#FF6800}{ 105 }$
$\color{#FF6800}{ 14 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 105 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 15 } } { \color{#FF6800}{ 2 } } }$
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