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Solve the equation
Answer
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Graph
$y = \dfrac { 1 } { 5 } x + 0.1$
$y = - 0.5 x + \dfrac { 3 } { 2 }$
$x$Intercept
$\left ( - \dfrac { 1 } { 2 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 1 } { 10 } \right )$
$x$Intercept
$\left ( 3 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 3 } { 2 } \right )$
$x = 2$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 5 } } } \color{#FF6800}{ x } + 0.1 = - 0.5 x + \dfrac { 3 } { 2 }$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 5 } } } + 0.1 = - 0.5 x + \dfrac { 3 } { 2 }$
$\dfrac { x } { 5 } + \color{#FF6800}{ 0.1 } = - 0.5 x + \dfrac { 3 } { 2 }$
$ $ Convert decimals to fractions $ $
$\dfrac { x } { 5 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 10 } } } = - 0.5 x + \dfrac { 3 } { 2 }$
$\dfrac { x } { 5 } + \dfrac { 1 } { 10 } = \color{#FF6800}{ - } \color{#FF6800}{ 0.5 } \color{#FF6800}{ x } + \dfrac { 3 } { 2 }$
$ $ Calculate the multiplication expression $ $
$\dfrac { x } { 5 } + \dfrac { 1 } { 10 } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } + \dfrac { 3 } { 2 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 5 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 10 } } } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 2 } } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 15 }$
$2 x + 1 = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } + 15$
$ $ Move the variable to the left-hand side and change the symbol $ $
$2 x + 1 \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ x } = 15$
$2 x \color{#FF6800}{ + } \color{#FF6800}{ 1 } + 5 x = 15$
$ $ Move the constant to the right side and change the sign $ $
$2 x + 5 x = 15 \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ x } = 15 - 1$
$ $ Organize the expression $ $
$\color{#FF6800}{ 7 } \color{#FF6800}{ x } = 15 - 1$
$7 x = \color{#FF6800}{ 15 } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$ $ Subtract $ 1 $ from $ 15$
$7 x = \color{#FF6800}{ 14 }$
$\color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ 14 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 2 }$
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