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Formula
Solve the equation
Graph
$y = \dfrac { x - 1 } { 3 }$
$y = \dfrac { 2 x + 3 } { 5 } - 1$
$x$Intercept
$\left ( 1 , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 1 } { 3 } \right )$
$x$Intercept
$\left ( 1 , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 2 } { 5 } \right )$
$\dfrac{ x-1 }{ 3 } = \dfrac{ 2x+3 }{ 5 } -1$
$x = 1$
 Solve a solution to $x$
$\dfrac { x - 1 } { 3 } = \dfrac { 2 x + 3 } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
 Convert an equation to a fraction using $a=\dfrac{a}{1}$
$\dfrac { x - 1 } { 3 } = \dfrac { 2 x + 3 } { 5 } + \color{#FF6800}{ \dfrac { - 1 } { 1 } }$
$\dfrac { x - 1 } { 3 } = \color{#FF6800}{ \dfrac { 2 x + 3 } { 5 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { - 1 } { 1 } }$
 Write all numerators above the least common denominator 
$\dfrac { x - 1 } { 3 } = \color{#FF6800}{ \dfrac { 2 x + 3 - 5 } { 5 } }$
$\dfrac { x - 1 } { 3 } = \dfrac { 2 x + \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } } { 5 }$
 Subtract $5$ from $3$
$\dfrac { x - 1 } { 3 } = \dfrac { 2 x \color{#FF6800}{ - } \color{#FF6800}{ 2 } } { 5 }$
$\color{#FF6800}{ \dfrac { x - 1 } { 3 } } = \color{#FF6800}{ \dfrac { 2 x - 2 } { 5 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) = \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
 Organize the expression 
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } = - 6 + 5$
 Organize the expression 
$\color{#FF6800}{ - } \color{#FF6800}{ x } = - 6 + 5$
$\color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 5 }$
 Organize the expression 
$\color{#FF6800}{ x } = \color{#FF6800}{ 1 }$
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