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Formula
Solve the equation
Graph
$y = \dfrac { x } { 2 } - \dfrac { 2 - x } { 6 }$
$y = 7$
$x$Intercept
$\left ( \dfrac { 1 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 1 } { 3 } \right )$
$\dfrac{ x }{ 2 } - \dfrac{ 2-x }{ 6 } = 7$
$x = 11$
 Solve a solution to $x$
$\dfrac { x } { 2 } - \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ x } } { 6 } = 7$
 Organize the expression 
$\dfrac { x } { 2 } - \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } { 6 } = 7$
$\color{#FF6800}{ \dfrac { x } { 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { - x + 2 } { 6 } } = \color{#FF6800}{ 7 }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) = \color{#FF6800}{ 42 }$
$3 x \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) = 42$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$3 x + \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = 42$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ x } - 2 = 42$
 Calculate between similar terms 
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } - 2 = 42$
$4 x \color{#FF6800}{ - } \color{#FF6800}{ 2 } = 42$
 Move the constant to the right side and change the sign 
$4 x = 42 \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
$4 x = \color{#FF6800}{ 42 } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
 Add $42$ and $2$
$4 x = \color{#FF6800}{ 44 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } = \color{#FF6800}{ 44 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } = \color{#FF6800}{ 11 }$
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