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Solve the equation
Answer
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Graph
$y = 0.2 \left ( x + 3 \right )$
$y = - \dfrac { 2 x + 5 } { 3 }$
$x$Intercept
$\left ( - 3 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 3 } { 5 } \right )$
$x$Intercept
$\left ( - \dfrac { 5 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 5 } { 3 } \right )$
$0.2 \left( x+3 \right) = - \dfrac{ 2x+5 }{ 3 }$
$x = - \dfrac { 34 } { 13 }$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 0.2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) = - \dfrac { 2 x + 5 } { 3 }$
$ $ Multiply each term in parentheses by $ 0.2$
$\color{#FF6800}{ 0.2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 0.2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = - \dfrac { 2 x + 5 } { 3 }$
$\color{#FF6800}{ 0.2 } \color{#FF6800}{ x } + 0.2 \times 3 = - \dfrac { 2 x + 5 } { 3 }$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { x } { 5 } } + 0.2 \times 3 = - \dfrac { 2 x + 5 } { 3 }$
$\dfrac { x } { 5 } + \color{#FF6800}{ 0.2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = - \dfrac { 2 x + 5 } { 3 }$
$ $ Multiply $ 0.2 $ and $ 3$
$\dfrac { x } { 5 } + \color{#FF6800}{ 0.6 } = - \dfrac { 2 x + 5 } { 3 }$
$\dfrac { x } { 5 } + \color{#FF6800}{ 0.6 } = - \dfrac { 2 x + 5 } { 3 }$
$ $ Convert decimals to fractions $ $
$\dfrac { x } { 5 } + \color{#FF6800}{ \dfrac { 3 } { 5 } } = - \dfrac { 2 x + 5 } { 3 }$
$\color{#FF6800}{ \dfrac { x } { 5 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 5 } } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 x + 5 } { 3 } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } = \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 25 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } = \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 25 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 25 } \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \color{#FF6800}{ x } = - 25 - 9$
$ $ Organize the expression $ $
$\color{#FF6800}{ 13 } \color{#FF6800}{ x } = - 25 - 9$
$13 x = \color{#FF6800}{ - } \color{#FF6800}{ 25 } \color{#FF6800}{ - } \color{#FF6800}{ 9 }$
$ $ Find the sum of the negative numbers $ $
$13 x = \color{#FF6800}{ - } \color{#FF6800}{ 34 }$
$\color{#FF6800}{ 13 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 34 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 34 } { 13 } }$
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