$2 x + 1 = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ x } + 35$
$ $ Calculate the multiplication expression $ $
$2 x + 1 = \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } + 35$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ + } \color{#FF6800}{ 35 }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } = \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 70 }$
$4 x + 2 = \color{#FF6800}{ x } + 70$
$ $ Move the variable to the left-hand side and change the symbol $ $
$4 x + 2 \color{#FF6800}{ - } \color{#FF6800}{ x } = 70$
$4 x \color{#FF6800}{ + } \color{#FF6800}{ 2 } - x = 70$
$ $ Move the constant to the right side and change the sign $ $
$4 x - x = 70 \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } = 70 - 2$
$ $ Organize the expression $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } = 70 - 2$
$3 x = \color{#FF6800}{ 70 } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$ $ Subtract $ 2 $ from $ 70$
$3 x = \color{#FF6800}{ 68 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } = \color{#FF6800}{ 68 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 68 } } { \color{#FF6800}{ 3 } } }$