$3 x + \color{#FF6800}{ \dfrac { 1 } { 3 } } \left ( \color{#FF6800}{ 100 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) = 100$
$ $ Multiply each term in parentheses by $ \dfrac { 1 } { 3 }$
$3 x + \color{#FF6800}{ \dfrac { 1 } { 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 100 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } } \color{#FF6800}{ x } = 100$
$3 x + \color{#FF6800}{ \dfrac { 1 } { 3 } } \color{#FF6800}{ \times } \color{#FF6800}{ 100 } - \dfrac { 1 } { 3 } x = 100$
$ $ Calculate the product of rational numbers $ $
$3 x + \color{#FF6800}{ \dfrac { 100 } { 3 } } - \dfrac { 1 } { 3 } x = 100$
$3 x + \dfrac { 100 } { 3 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 3 } } \color{#FF6800}{ x } = 100$
$ $ Calculate the multiplication expression $ $
$3 x + \dfrac { 100 } { 3 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 3 } } = 100$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } - \dfrac { x } { 3 } + \dfrac { 100 } { 3 } = 100$
$ $ Convert an equation to a fraction using $ a=\dfrac{a}{1}$
$\color{#FF6800}{ \dfrac { 3 x } { 1 } } - \dfrac { x } { 3 } + \dfrac { 100 } { 3 } = 100$
$\color{#FF6800}{ \dfrac { 3 x } { 1 } } - \dfrac { x } { 3 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 100 } { 3 } } = 100$
$ $ Write all numerators above the least common denominator $ $
$\color{#FF6800}{ \dfrac { 9 x + 100 } { 3 } } - \dfrac { x } { 3 } = 100$
$\color{#FF6800}{ \dfrac { 9 x + 100 } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 3 } } = \color{#FF6800}{ 100 }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 100 } \color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ 300 }$
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 100 } \color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ 300 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ 8 } \color{#FF6800}{ x } = \color{#FF6800}{ 200 }$
$\color{#FF6800}{ 8 } \color{#FF6800}{ x } = \color{#FF6800}{ 200 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 25 }$