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Solve the equation
Answer
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Graph
$y = 0.2 \left ( x + 3 \right )$
$y = 0.3 x - 5$
$x$Intercept
$\left ( - 3 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 3 } { 5 } \right )$
$x$Intercept
$\left ( \dfrac { 50 } { 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 5 \right )$
$0.2 \left( x+3 \right) = 0.3x-5$
$x = 56$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 0.2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) = 0.3 x - 5$
$ $ Multiply each term in parentheses by $ 0.2$
$\color{#FF6800}{ 0.2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 0.2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = 0.3 x - 5$
$\color{#FF6800}{ 0.2 } \color{#FF6800}{ x } + 0.2 \times 3 = 0.3 x - 5$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { x } { 5 } } + 0.2 \times 3 = 0.3 x - 5$
$\dfrac { x } { 5 } + \color{#FF6800}{ 0.2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = 0.3 x - 5$
$ $ Multiply $ 0.2 $ and $ 3$
$\dfrac { x } { 5 } + \color{#FF6800}{ 0.6 } = 0.3 x - 5$
$\dfrac { x } { 5 } + \color{#FF6800}{ 0.6 } = 0.3 x - 5$
$ $ Convert decimals to fractions $ $
$\dfrac { x } { 5 } + \color{#FF6800}{ \dfrac { 3 } { 5 } } = 0.3 x - 5$
$\dfrac { x } { 5 } + \dfrac { 3 } { 5 } = \color{#FF6800}{ 0.3 } \color{#FF6800}{ x } - 5$
$ $ Calculate the multiplication expression $ $
$\dfrac { x } { 5 } + \dfrac { 3 } { 5 } = \color{#FF6800}{ \dfrac { 3 x } { 10 } } - 5$
$\color{#FF6800}{ \dfrac { x } { 5 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 5 } } = \color{#FF6800}{ \dfrac { 3 x } { 10 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 6 } = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 50 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 6 } = \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 50 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 50 } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = - 50 - 6$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ x } = - 50 - 6$
$- x = \color{#FF6800}{ - } \color{#FF6800}{ 50 } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ Find the sum of the negative numbers $ $
$- x = \color{#FF6800}{ - } \color{#FF6800}{ 56 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 56 }$
$ $ Change the sign of both sides of the equation $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 56 } \right )$
$x = \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 56 \right )$
$ $ Simplify Minus $ $
$x = 56$
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