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Formula
Solve the equation
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$y = \dfrac { x + 1 } { 3 } - \dfrac { x - 3 } { 2 }$
$y = 1$
$x$-intercept
$\left ( 11 , 0 \right )$
$y$-intercept
$\left ( 0 , \dfrac { 11 } { 6 } \right )$
$\dfrac{ x+1 }{ 3 } - \dfrac{ x-3 }{ 2 } = 1$
$x = 5$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { x + 1 } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x - 3 } { 2 } } = 1$
 Write all numerators above the least common denominator 
$\color{#FF6800}{ \dfrac { 2 x + 2 - 3 x + 9 } { 6 } } = 1$
$\dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 2 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 9 } { 6 } = 1$
 Calculate between similar terms 
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ x } + 2 + 9 } { 6 } = 1$
$\dfrac { - x + \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 9 } } { 6 } = 1$
 Add $2$ and $9$
$\dfrac { - x + \color{#FF6800}{ 11 } } { 6 } = 1$
$\color{#FF6800}{ \dfrac { - x + 11 } { 6 } } = \color{#FF6800}{ 1 }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 11 } = \color{#FF6800}{ 6 }$
$- x \color{#FF6800}{ + } \color{#FF6800}{ 11 } = 6$
 Move the constant to the right side and change the sign 
$- x = 6 \color{#FF6800}{ - } \color{#FF6800}{ 11 }$
$- x = \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 11 }$
 Subtract $11$ from $6$
$- x = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
 Change the sign of both sides of the equation 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right )$
$x = \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 5 \right )$
 Simplify Minus 
$x = 5$
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