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Formula
Solve the equation
Graph
$y = \dfrac { 3 x + 5 } { 6 } - \dfrac { x - 1 } { 8 }$
$y = 1$
$x$Intercept
$\left ( - \dfrac { 23 } { 9 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 23 } { 24 } \right )$
$\dfrac{ 3x+5 }{ 6 } - \dfrac{ x-1 }{ 8 } = 1$
$x = \dfrac { 1 } { 9 }$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { 3 x + 5 } { 6 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x - 1 } { 8 } } = 1$
 Write all numerators above the least common denominator 
$\color{#FF6800}{ \dfrac { 12 x + 20 - 3 x + 3 } { 24 } } = 1$
$\dfrac { \color{#FF6800}{ 12 } \color{#FF6800}{ x } + 20 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 3 } { 24 } = 1$
 Calculate between similar terms 
$\dfrac { \color{#FF6800}{ 9 } \color{#FF6800}{ x } + 20 + 3 } { 24 } = 1$
$\dfrac { 9 x + \color{#FF6800}{ 20 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } } { 24 } = 1$
 Add $20$ and $3$
$\dfrac { 9 x + \color{#FF6800}{ 23 } } { 24 } = 1$
$\color{#FF6800}{ \dfrac { 9 x + 23 } { 24 } } = \color{#FF6800}{ 1 }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 23 } = \color{#FF6800}{ 24 }$
$9 x \color{#FF6800}{ + } \color{#FF6800}{ 23 } = 24$
 Move the constant to the right side and change the sign 
$9 x = 24 \color{#FF6800}{ - } \color{#FF6800}{ 23 }$
$9 x = \color{#FF6800}{ 24 } \color{#FF6800}{ - } \color{#FF6800}{ 23 }$
 Subtract $23$ from $24$
$9 x = \color{#FF6800}{ 1 }$
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } = \color{#FF6800}{ 1 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 1 } { 9 } }$
$x = \dfrac { 1 } { 9 }$
Solve the fractional equation
$\color{#FF6800}{ \dfrac { 3 x + 5 } { 6 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x - 1 } { 8 } } = \color{#FF6800}{ 1 }$
 Solve a solution to $x$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 1 } { 9 } }$
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