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Solve the inequality
Answer
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$\dfrac { x - 2 } { 4 } - \dfrac { 2 x - 1 } { 5 } < 0$
$\dfrac { x - 2 } { 4 } - \dfrac { 2 x - 1 } { 5 } < 0$
Solution of inequality
$x > - 2$
$\dfrac{ x-2 }{ 4 } - \dfrac{ 2x-1 }{ 5 } < 0$
$x > - 2$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ \dfrac { x - 2 } { 4 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 2 x - 1 } { 5 } } < 0$
$ $ Write all numerators above the least common denominator $ $
$\color{#FF6800}{ \dfrac { 5 x - 10 - 8 x + 4 } { 20 } } < 0$
$\dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ x } - 10 \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } + 4 } { 20 } < 0$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } - 10 + 4 } { 20 } < 0$
$\dfrac { - 3 x \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } } { 20 } < 0$
$ $ Add $ - 10 $ and $ 4$
$\dfrac { - 3 x \color{#FF6800}{ - } \color{#FF6800}{ 6 } } { 20 } < 0$
$\color{#FF6800}{ \dfrac { - 3 x - 6 } { 20 } } < \color{#FF6800}{ 0 }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } < \color{#FF6800}{ 0 }$
$- 3 x \color{#FF6800}{ - } \color{#FF6800}{ 6 } < 0$
$ $ Move the constant to the right side and change the sign $ $
$- 3 x < \color{#FF6800}{ 6 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } < \color{#FF6800}{ 6 }$
$ $ Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction $ $
$3 x > - 6$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
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