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Solve the equation
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$y = \dfrac { 1 } { 2 } x - \dfrac { x - 1 } { 3 }$
$y = 1$
$x$Intercept
$\left ( - 2 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 1 } { 3 } \right )$
$\dfrac{ 1 }{ 2 } x- \dfrac{ x-1 }{ 3 } = 1$
$x = 4$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } - \dfrac { x - 1 } { 3 } = 1$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { x } { 2 } } - \dfrac { x - 1 } { 3 } = 1$
$\color{#FF6800}{ \dfrac { x } { 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x - 1 } { 3 } } = \color{#FF6800}{ 1 }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \right ) = \color{#FF6800}{ 6 }$
$3 x - \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \right ) = 6$
 Multiply each term in parentheses by $2$
$3 x - \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) = 6$
$3 x \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) = 6$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$3 x \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + \color{#FF6800}{ 2 } = 6$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 2 = 6$
 Calculate between similar terms 
$\color{#FF6800}{ x } + 2 = 6$
$x \color{#FF6800}{ + } \color{#FF6800}{ 2 } = 6$
 Move the constant to the right side and change the sign 
$x = 6 \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$x = \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
 Subtract $2$ from $6$
$x = \color{#FF6800}{ 4 }$
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