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Solve the equation

Answer

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$y = \dfrac { 5 } { 6 } x + 1$

$y = 0.5 x + \dfrac { 7 } { 6 }$

$x$Intercept

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

$y$Intercept

$\left ( 0 , 1 \right )$

$x$Intercept

$\left ( - \dfrac { 7 } { 3 } , 0 \right )$

$y$Intercept

$\left ( 0 , \dfrac { 7 } { 6 } \right )$

$x = \dfrac { 1 } { 2 }$

$ $ Solve a solution to $ x$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ x } + 1 = 0.5 x + \dfrac { 7 } { 6 }$

$ $ Calculate the multiplication expression $ $

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ x } } { \color{#FF6800}{ 6 } } } + 1 = 0.5 x + \dfrac { 7 } { 6 }$

$\dfrac { 5 x } { 6 } + 1 = \color{#FF6800}{ 0.5 } \color{#FF6800}{ x } + \dfrac { 7 } { 6 }$

$ $ Calculate the multiplication expression $ $

$\dfrac { 5 x } { 6 } + 1 = \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } + \dfrac { 7 } { 6 }$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ x } } { \color{#FF6800}{ 6 } } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } } { \color{#FF6800}{ 6 } } }$

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

$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 6 } = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 }$

$5 x + 6 = \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 7$

$ $ Move the variable to the left-hand side and change the symbol $ $

$5 x + 6 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 7$

$5 x \color{#FF6800}{ + } \color{#FF6800}{ 6 } - 3 x = 7$

$ $ Move the constant to the right side and change the sign $ $

$5 x - 3 x = 7 \color{#FF6800}{ - } \color{#FF6800}{ 6 }$

$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 7 - 6$

$ $ Organize the expression $ $

$\color{#FF6800}{ 2 } \color{#FF6800}{ x } = 7 - 6$

$2 x = \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$

$ $ Subtract $ 6 $ from $ 7$

$2 x = \color{#FF6800}{ 1 }$