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Formula
Solve the equation
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
$\left ( 0 , - 9 \right )$
$\dfrac{ 1 }{ 3 } x-2 = - \dfrac{ 3 }{ 5 } x-9$
$x = - \dfrac { 15 } { 2 }$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { 1 } { 3 } } \color{#FF6800}{ x } - 2 = - \dfrac { 3 } { 5 } x - 9$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { x } { 3 } } - 2 = - \dfrac { 3 } { 5 } x - 9$
$\dfrac { x } { 3 } - 2 = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 5 } } \color{#FF6800}{ x } - 9$
 Calculate the multiplication expression 
$\dfrac { x } { 3 } - 2 = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 x } { 5 } } - 9$
$\color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
 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 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 15 } { 2 } }$
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