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Solve the inequality
Graph
$\dfrac { x } { 9 } + \dfrac { 8 - x } { 4 } \leq \dfrac { 7 } { 6 }$
$\dfrac { x } { 9 } + \dfrac { 8 - x } { 4 } \leq \dfrac { 7 } { 6 }$
Solution of inequality
$x \geq 6$
$\dfrac{ x }{ 9 } + \dfrac{ 8-x }{ 4 } \leq \dfrac{ 7 }{ 6 }$
$x \geq 6$
 Solve a solution to $x$
$\dfrac { x } { 9 } + \dfrac { \color{#FF6800}{ 8 } \color{#FF6800}{ - } \color{#FF6800}{ x } } { 4 } \leq \dfrac { 7 } { 6 }$
 Organize the expression 
$\dfrac { x } { 9 } + \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } } { 4 } \leq \dfrac { 7 } { 6 }$
$\color{#FF6800}{ \dfrac { x } { 9 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { - x + 8 } { 4 } } \leq \color{#FF6800}{ \dfrac { 7 } { 6 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \leq \color{#FF6800}{ 42 }$
$4 x + \color{#FF6800}{ 9 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \right ) \leq 42$
 Multiply each term in parentheses by $9$
$4 x \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ x } + \color{#FF6800}{ 9 } \color{#FF6800}{ \times } \color{#FF6800}{ 8 } \leq 42$
$4 x - 9 x + \color{#FF6800}{ 9 } \color{#FF6800}{ \times } \color{#FF6800}{ 8 } \leq 42$
 Multiply $9$ and $8$
$4 x - 9 x + \color{#FF6800}{ 72 } \leq 42$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ x } + 72 \leq 42$
 Calculate between similar terms 
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } + 72 \leq 42$
$- 5 x \color{#FF6800}{ + } \color{#FF6800}{ 72 } \leq 42$
 Move the constant to the right side and change the sign 
$- 5 x \leq 42 \color{#FF6800}{ - } \color{#FF6800}{ 72 }$
$- 5 x \leq \color{#FF6800}{ 42 } \color{#FF6800}{ - } \color{#FF6800}{ 72 }$
 Subtract $72$ from $42$
$- 5 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 30 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ 30 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$5 x \geq 30$
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \geq \color{#FF6800}{ 30 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } \geq \color{#FF6800}{ 6 }$
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