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Solve the inequality
Answer
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Graph
$0.2 x - \dfrac { 1 } { 5 } < \dfrac { 1 } { 2 } x + 1.3$
$0.2 x - \dfrac { 1 } { 5 } < \dfrac { 1 } { 2 } x + 1.3$
Solution of inequality
$x > - 5$
$x > - 5$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 0.2 } \color{#FF6800}{ x } - \dfrac { 1 } { 5 } < \dfrac { 1 } { 2 } x + 1.3$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 5 } } } - \dfrac { 1 } { 5 } < \dfrac { 1 } { 2 } x + 1.3$
$\dfrac { x } { 5 } - \dfrac { 1 } { 5 } < \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ x } + 1.3$
$ $ Calculate the multiplication expression $ $
$\dfrac { x } { 5 } - \dfrac { 1 } { 5 } < \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } + 1.3$
$\dfrac { x } { 5 } - \dfrac { 1 } { 5 } < \dfrac { x } { 2 } + \color{#FF6800}{ 1.3 }$
$ $ Convert decimals to fractions $ $
$\dfrac { x } { 5 } - \dfrac { 1 } { 5 } < \dfrac { x } { 2 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 13 } } { \color{#FF6800}{ 10 } } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 5 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 5 } } } < \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 13 } } { \color{#FF6800}{ 10 } } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } < \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 13 }$
$2 x - 2 < \color{#FF6800}{ 5 } \color{#FF6800}{ x } + 13$
$ $ Move the variable to the left-hand side and change the symbol $ $
$2 x - 2 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } < 13$
$2 x \color{#FF6800}{ - } \color{#FF6800}{ 2 } - 5 x < 13$
$ $ Move the constant to the right side and change the sign $ $
$2 x - 5 x < 13 \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } < 13 + 2$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } < 13 + 2$
$- 3 x < \color{#FF6800}{ 13 } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
$ $ Add $ 13 $ and $ 2$
$- 3 x < \color{#FF6800}{ 15 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } < \color{#FF6800}{ 15 }$
$ $ Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction $ $
$3 x > - 15$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 15 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
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