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Solve the equation
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$y = \dfrac { x } { 6 } - \dfrac { x + 5 } { 8 }$
$y = 1$
$x$-intercept
$\left ( 15 , 0 \right )$
$y$-intercept
$\left ( 0 , - \dfrac { 5 } { 8 } \right )$
$\dfrac{ x }{ 6 } - \dfrac{ x+5 }{ 8 } = 1$
$x = 39$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { x } { 6 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x + 5 } { 8 } } = \color{#FF6800}{ 1 }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right ) \right ) = \color{#FF6800}{ 24 }$
$4 x - \left ( \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right ) \right ) = 24$
 Multiply each term in parentheses by $3$
$4 x - \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \right ) = 24$
$4 x - \left ( 3 x + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } \right ) = 24$
 Multiply $3$ and $5$
$4 x - \left ( 3 x + \color{#FF6800}{ 15 } \right ) = 24$
$4 x \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \right ) = 24$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$4 x \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 15 } = 24$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } - 15 = 24$
 Calculate between similar terms 
$\color{#FF6800}{ x } - 15 = 24$
$x \color{#FF6800}{ - } \color{#FF6800}{ 15 } = 24$
 Move the constant to the right side and change the sign 
$x = 24 \color{#FF6800}{ + } \color{#FF6800}{ 15 }$
$x = \color{#FF6800}{ 24 } \color{#FF6800}{ + } \color{#FF6800}{ 15 }$
 Add $24$ and $15$
$x = \color{#FF6800}{ 39 }$
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