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Solve the equation

Answer

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$y = \dfrac { 3 x } { 4 } - \dfrac { 2 x + 1 } { 3 }$

$y = 1$

$x$Intercept

$\left ( 4 , 0 \right )$

$y$Intercept

$\left ( 0 , - \dfrac { 1 } { 3 } \right )$

$x = 16$

$ $ Solve a solution to $ x$

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

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

$\color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \right ) = \color{#FF6800}{ 12 }$

$3 \left ( 3 x \right ) - \left ( \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \right ) = 12$

$ $ Multiply each term in parentheses by $ 4$

$3 \left ( 3 x \right ) - \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) = 12$

$\color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) - \left ( 4 \times 2 x + 4 \right ) = 12$

$ $ Get rid of unnecessary parentheses $ $

$\color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ x } - \left ( 4 \times 2 x + 4 \right ) = 12$

$\color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ x } - \left ( 4 \times 2 x + 4 \right ) = 12$

$ $ Simplify the expression $ $

$\color{#FF6800}{ 9 } \color{#FF6800}{ x } - \left ( 4 \times 2 x + 4 \right ) = 12$

$9 x - \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 4 \right ) = 12$

$ $ Simplify the expression $ $

$9 x - \left ( \color{#FF6800}{ 8 } \color{#FF6800}{ x } + 4 \right ) = 12$

$9 x \color{#FF6800}{ - } \left ( \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) = 12$

$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $

$9 x \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } = 12$

$\color{#FF6800}{ 9 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } - 4 = 12$

$ $ Calculate between similar terms $ $

$\color{#FF6800}{ x } - 4 = 12$

$x \color{#FF6800}{ - } \color{#FF6800}{ 4 } = 12$

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

$x = 12 \color{#FF6800}{ + } \color{#FF6800}{ 4 }$

$x = \color{#FF6800}{ 12 } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$

$ $ Add $ 12 $ and $ 4$

$x = \color{#FF6800}{ 16 }$

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