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Formula
Solve the equation
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$y = \dfrac { x - 2 } { 3 } - \dfrac { 2 x + 3 } { 5 }$
$y = - 1$
$x$-intercept
$\left ( - 19 , 0 \right )$
$y$-intercept
$\left ( 0 , - \dfrac { 19 } { 15 } \right )$
$\dfrac{ x-2 }{ 3 } - \dfrac{ 2x+3 }{ 5 } = -1$
$x = - 4$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { x - 2 } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 x + 3 } { 5 } } = - 1$
 Write all numerators above the least common denominator 
$\color{#FF6800}{ \dfrac { 5 x - 10 - 6 x - 9 } { 15 } } = - 1$
$\dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ x } - 10 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } - 9 } { 15 } = - 1$
 Calculate between similar terms 
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ x } - 10 - 9 } { 15 } = - 1$
$\dfrac { - x \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 9 } } { 15 } = - 1$
 Find the sum of the negative numbers 
$\dfrac { - x \color{#FF6800}{ - } \color{#FF6800}{ 19 } } { 15 } = - 1$
$\color{#FF6800}{ \dfrac { - x - 19 } { 15 } } = \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 19 } = \color{#FF6800}{ - } \color{#FF6800}{ 15 }$
$- x \color{#FF6800}{ - } \color{#FF6800}{ 19 } = - 15$
 Move the constant to the right side and change the sign 
$- x = - 15 \color{#FF6800}{ + } \color{#FF6800}{ 19 }$
$- x = \color{#FF6800}{ - } \color{#FF6800}{ 15 } \color{#FF6800}{ + } \color{#FF6800}{ 19 }$
 Add $- 15$ and $19$
$- x = \color{#FF6800}{ 4 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ 4 }$
 Change the sign of both sides of the equation 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
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