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Solve the equation
Answer
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Graph
$y = \dfrac { 1 } { 2 } x + \dfrac { 3 } { 2 }$
$x$Intercept
$\left ( - 3 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 3 } { 2 } \right )$
$x = 2 y - 3$
$ $ Solve a solution to $ x$
$y = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ x } + \dfrac { 3 } { 2 }$
$ $ Calculate the multiplication expression $ $
$y = \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } + \dfrac { 3 } { 2 }$
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 2 } } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ y } = \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$2 y = \color{#FF6800}{ x } + 3$
$ $ Move $ x $ term to the left side and change the sign $ $
$2 y - x = 3$
$\color{#FF6800}{ 2 } \color{#FF6800}{ y } - x = 3$
$ $ Move the rest of the expression except $ x $ term to the right side and replace the sign $ $
$- x = 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right )$
$- x = \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ y } \right )$
$ $ Organize the expression $ $
$- x = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$ $ Change the sign of both sides of the equation $ $
$x = 2 y - 3$
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