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Formula
Solve the inequality
Graph
$\dfrac { x - 4 } { 3 } - \dfrac { 3 x - 5 } { 4 } < 2$
$\dfrac { x - 4 } { 3 } - \dfrac { 3 x - 5 } { 4 } < 2$
Solution of inequality
$x > - 5$
$\dfrac{ x-4 }{ 3 } - \dfrac{ 3x-5 }{ 4 } < 2$
$x > - 5$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { x - 4 } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 x - 5 } { 4 } } < 2$
 Write all numerators above the least common denominator 
$\color{#FF6800}{ \dfrac { 4 x - 16 - 9 x + 15 } { 12 } } < 2$
$\dfrac { \color{#FF6800}{ 4 } \color{#FF6800}{ x } - 16 \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ x } + 15 } { 12 } < 2$
 Calculate between similar terms 
$\dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } - 16 + 15 } { 12 } < 2$
$\dfrac { - 5 x \color{#FF6800}{ - } \color{#FF6800}{ 16 } \color{#FF6800}{ + } \color{#FF6800}{ 15 } } { 12 } < 2$
 Add $- 16$ and $15$
$\dfrac { - 5 x \color{#FF6800}{ - } \color{#FF6800}{ 1 } } { 12 } < 2$
$\color{#FF6800}{ \dfrac { - 5 x - 1 } { 12 } } < \color{#FF6800}{ 2 }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } < \color{#FF6800}{ 24 }$
$- 5 x \color{#FF6800}{ - } \color{#FF6800}{ 1 } < 24$
 Move the constant to the right side and change the sign 
$- 5 x < 24 \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
$- 5 x < \color{#FF6800}{ 24 } \color{#FF6800}{ + } \color{#FF6800}{ 1 }$
 Add $24$ and $1$
$- 5 x < \color{#FF6800}{ 25 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } < \color{#FF6800}{ 25 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$5 x > - 25$
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 25 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
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Inequality
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