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Solve the inequality

Answer

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$\dfrac { x } { 12 } + \dfrac { 20 - x } { 4 } \leq 3$

Solution of inequality

$x \geq 12$

$ $ Solve a solution to $ x$

$\dfrac { x } { 12 } + \dfrac { \color{#FF6800}{ 20 } \color{#FF6800}{ - } \color{#FF6800}{ x } } { 4 } \leq 3$

$ $ Organize the expression $ $

$\dfrac { x } { 12 } + \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 20 } } { 4 } \leq 3$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 12 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 20 } } { \color{#FF6800}{ 4 } } } \leq \color{#FF6800}{ 3 }$

$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $

$\color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 20 } \right ) \leq \color{#FF6800}{ 36 }$

$x + \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 20 } \right ) \leq 36$

$ $ Multiply each term in parentheses by $ 3$

$x \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 20 } \leq 36$

$x - 3 x + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 20 } \leq 36$

$ $ Multiply $ 3 $ and $ 20$

$x - 3 x + \color{#FF6800}{ 60 } \leq 36$

$\color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 60 \leq 36$

$ $ Calculate between similar terms $ $

$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 60 \leq 36$

$- 2 x \color{#FF6800}{ + } \color{#FF6800}{ 60 } \leq 36$

$ $ Move the constant to the right side and change the sign $ $

$- 2 x \leq 36 \color{#FF6800}{ - } \color{#FF6800}{ 60 }$

$- 2 x \leq \color{#FF6800}{ 36 } \color{#FF6800}{ - } \color{#FF6800}{ 60 }$

$ $ Subtract $ 60 $ from $ 36$

$- 2 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 24 }$

$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ 24 }$

$ $ Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction $ $

$2 x \geq 24$

$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq \color{#FF6800}{ 24 }$

$ $ Divide both sides by the same number $ $

$\color{#FF6800}{ x } \geq \color{#FF6800}{ 12 }$

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