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Solve the equation
Answer
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Graph
$y = \dfrac { 1 } { 3 } x - 2$
$y = \dfrac { 5 } { 3 } - x$
$x$Intercept
$\left ( 6 , 0 \right )$
$y$Intercept
$\left ( 0 , - 2 \right )$
$x$Intercept
$\left ( \dfrac { 5 } { 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 5 } { 3 } \right )$
$\dfrac{ 1 }{ 3 } x-2 = \dfrac{ 5 }{ 3 } -x$
$x = \dfrac { 11 } { 4 }$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ \dfrac { 1 } { 3 } } \color{#FF6800}{ x } - 2 = \dfrac { 5 } { 3 } - x$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { x } { 3 } } - 2 = \dfrac { 5 } { 3 } - x$
$\color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = \color{#FF6800}{ \dfrac { 5 } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ x }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 }$
$x - 6 = \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 5$
$ $ Move the variable to the left-hand side and change the symbol $ $
$x - 6 \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 5$
$x \color{#FF6800}{ - } \color{#FF6800}{ 6 } + 3 x = 5$
$ $ Move the constant to the right side and change the sign $ $
$x + 3 x = 5 \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 5 + 6$
$ $ Organize the expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } = 5 + 6$
$4 x = \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$ $ Add $ 5 $ and $ 6$
$4 x = \color{#FF6800}{ 11 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } = \color{#FF6800}{ 11 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 11 } { 4 } }$
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