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Solve the equation
Answer
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Graph
$y = 3.2 x - 2.6$
$y = 0.8 x - 1$
$x$Intercept
$\left ( \dfrac { 13 } { 16 } , 0 \right )$
$y$Intercept
$\left ( 0 , - \dfrac { 13 } { 5 } \right )$
$x$Intercept
$\left ( \dfrac { 5 } { 4 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 1 \right )$
$3.2x-2.6 = 0.8x-1$
$x = \dfrac { 2 } { 3 }$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 3.2 } \color{#FF6800}{ x } - 2.6 = 0.8 x - 1$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { 16 x } { 5 } } - 2.6 = 0.8 x - 1$
$\dfrac { 16 x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2.6 } = 0.8 x - 1$
$ $ Convert decimals to fractions $ $
$\dfrac { 16 x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 13 } { 5 } } = 0.8 x - 1$
$\dfrac { 16 x } { 5 } - \dfrac { 13 } { 5 } = \color{#FF6800}{ 0.8 } \color{#FF6800}{ x } - 1$
$ $ Calculate the multiplication expression $ $
$\dfrac { 16 x } { 5 } - \dfrac { 13 } { 5 } = \color{#FF6800}{ \dfrac { 4 x } { 5 } } - 1$
$\color{#FF6800}{ \dfrac { 16 x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 13 } { 5 } } = \color{#FF6800}{ \dfrac { 4 x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 16 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 13 } = \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$16 x - 13 = \color{#FF6800}{ 4 } \color{#FF6800}{ x } - 5$
$ $ Move the variable to the left-hand side and change the symbol $ $
$16 x - 13 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } = - 5$
$16 x \color{#FF6800}{ - } \color{#FF6800}{ 13 } - 4 x = - 5$
$ $ Move the constant to the right side and change the sign $ $
$16 x - 4 x = - 5 \color{#FF6800}{ + } \color{#FF6800}{ 13 }$
$\color{#FF6800}{ 16 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } = - 5 + 13$
$ $ Organize the expression $ $
$\color{#FF6800}{ 12 } \color{#FF6800}{ x } = - 5 + 13$
$12 x = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 13 }$
$ $ Add $ - 5 $ and $ 13$
$12 x = \color{#FF6800}{ 8 }$
$\color{#FF6800}{ 12 } \color{#FF6800}{ x } = \color{#FF6800}{ 8 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 2 } { 3 } }$
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