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Formula
Solve the inequality
Graph
$\dfrac { 4 - x } { 2 } \leq 3 - \dfrac { x } { 4 }$
$\dfrac { 4 - x } { 2 } \leq 3 - \dfrac { x } { 4 }$
Solution of inequality
$x \geq - 4$
$\dfrac{ 4-x }{ 2 } \leq 3- \dfrac{ x }{ 4 }$
$x \geq - 4$
 Solve a solution to $x$
$\dfrac { \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ x } } { 2 } \leq 3 - \dfrac { x } { 4 }$
 Organize the expression 
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } } { 2 } \leq 3 - \dfrac { x } { 4 }$
$\color{#FF6800}{ \dfrac { - x + 4 } { 2 } } \leq \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 4 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \leq \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 12 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \leq - x + 12$
 Multiply each term in parentheses by $2$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \leq - x + 12$
$- 2 x + \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \leq - x + 12$
 Multiply $2$ and $4$
$- 2 x + \color{#FF6800}{ 8 } \leq - x + 12$
$- 2 x + 8 \leq \color{#FF6800}{ - } \color{#FF6800}{ x } + 12$
 Move the variable to the left-hand side and change the symbol 
$- 2 x + 8 \color{#FF6800}{ + } \color{#FF6800}{ x } \leq 12$
$- 2 x \color{#FF6800}{ + } \color{#FF6800}{ 8 } + x \leq 12$
 Move the constant to the right side and change the sign 
$- 2 x + x \leq 12 \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ x } \leq 12 - 8$
 Organize the expression 
$\color{#FF6800}{ - } \color{#FF6800}{ x } \leq 12 - 8$
$- x \leq \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
 Subtract $8$ from $12$
$- x \leq \color{#FF6800}{ 4 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } \leq \color{#FF6800}{ 4 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$\color{#FF6800}{ x } \geq \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
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