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$\color{#FF6800}{ \dfrac { x + 1 } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x - 3 } { 2 } } = 1$

$ $ 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 $ $

$x = 5$