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Solve the equation

Answer

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$y = \dfrac { 2 x + 3 } { 6 } - \dfrac { 3 } { 4 } x$

$y = \dfrac { 1 } { 4 }$

$x$Intercept

$\left ( \dfrac { 6 } { 5 } , 0 \right )$

$y$Intercept

$\left ( 0 , \dfrac { 1 } { 2 } \right )$

$x = \dfrac { 3 } { 5 }$

$ $ Solve a solution to $ x$

$\dfrac { 2 x + 3 } { 6 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 4 } } } \color{#FF6800}{ x } = \dfrac { 1 } { 4 }$

$ $ Calculate the multiplication expression $ $

$\dfrac { 2 x + 3 } { 6 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 4 } } } = \dfrac { 1 } { 4 }$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 4 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 4 } } }$

$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $

$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) \right ) = \color{#FF6800}{ 3 }$

$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) \right ) = \color{#FF6800}{ 3 }$

$ $ Organize the expression $ $

$\color{#FF6800}{ 5 } \color{#FF6800}{ x } = \color{#FF6800}{ 3 }$

$\color{#FF6800}{ 5 } \color{#FF6800}{ x } = \color{#FF6800}{ 3 }$

$ $ Divide both sides by the same number $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 5 } } }$

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