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