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Solve the equation
$$y = 2 x - 1$$
$x = \dfrac { 1 } { 2 } y + \dfrac { 1 } { 2 }$
 Solve a solution to $x$
$y = \color{#FF6800}{ 2 } \color{#FF6800}{ x } - 1$
 Move $x$ term to the left side and change the sign 
$y \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } = - 1$
$\color{#FF6800}{ y } - 2 x = - 1$
 Move the rest of the expression except $x$ term to the right side and replace the sign 
$- 2 x = - 1 \color{#FF6800}{ - } \color{#FF6800}{ y }$
$- 2 x = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ y }$
 Organize the expression 
$- 2 x = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ y } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
 Change the sign of both sides of the equation 
$2 x = y + 1$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } = \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } = \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 2 }$
$x = \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 2 }$
 Convert division to multiplication 
$x = \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
$x = \left ( \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
 Multiply each term in parentheses by $\dfrac { 1 } { 2 }$
$x = \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
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