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Solve the inequality
Answer
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Graph
$0.3 x + \dfrac { 2 } { 5 } < \dfrac { x + 2 } { 2 }$
$0.3 x + \dfrac { 2 } { 5 } < \dfrac { x + 2 } { 2 }$
Solution of inequality
$x > - 3$
$x > - 3$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 0.3 } \color{#FF6800}{ x } + \dfrac { 2 } { 5 } < \dfrac { x + 2 } { 2 }$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } } + \dfrac { 2 } { 5 } < \dfrac { x + 2 } { 2 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 5 } } } < \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } { \color{#FF6800}{ 2 } } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } < \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$3 x + 4 < \color{#FF6800}{ 5 } \color{#FF6800}{ x } + 10$
$ $ Move the variable to the left-hand side and change the symbol $ $
$3 x + 4 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } < 10$
$3 x \color{#FF6800}{ + } \color{#FF6800}{ 4 } - 5 x < 10$
$ $ Move the constant to the right side and change the sign $ $
$3 x - 5 x < 10 \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } < 10 - 4$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } < 10 - 4$
$- 2 x < \color{#FF6800}{ 10 } \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$ $ Subtract $ 4 $ from $ 10$
$- 2 x < \color{#FF6800}{ 6 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } < \color{#FF6800}{ 6 }$
$ $ Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction $ $
$2 x > - 6$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
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