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Formula
Solve the inequality
Graph
$0.2 x - \dfrac { 1 } { 5 } < \dfrac { 1 } { 2 } x + 1.3$
$0.2 x - \dfrac { 1 } { 5 } < \dfrac { 1 } { 2 } x + 1.3$
Solution of inequality
$x > - 5$
$0.2x- \dfrac{ 1 }{ 5 } < \dfrac{ 1 }{ 2 } x+1.3$
$x > - 5$
 Solve a solution to $x$
$\color{#FF6800}{ 0.2 } \color{#FF6800}{ x } - \dfrac { 1 } { 5 } < \dfrac { 1 } { 2 } x + 1.3$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { x } { 5 } } - \dfrac { 1 } { 5 } < \dfrac { 1 } { 2 } x + 1.3$
$\dfrac { x } { 5 } - \dfrac { 1 } { 5 } < \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } + 1.3$
 Calculate the multiplication expression 
$\dfrac { x } { 5 } - \dfrac { 1 } { 5 } < \color{#FF6800}{ \dfrac { x } { 2 } } + 1.3$
$\dfrac { x } { 5 } - \dfrac { 1 } { 5 } < \dfrac { x } { 2 } + \color{#FF6800}{ 1.3 }$
 Convert decimals to fractions 
$\dfrac { x } { 5 } - \dfrac { 1 } { 5 } < \dfrac { x } { 2 } + \color{#FF6800}{ \dfrac { 13 } { 10 } }$
$\color{#FF6800}{ \dfrac { x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 5 } } < \color{#FF6800}{ \dfrac { x } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 13 } { 10 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } < \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 13 }$
$2 x - 2 < \color{#FF6800}{ 5 } \color{#FF6800}{ x } + 13$
 Move the variable to the left-hand side and change the symbol 
$2 x - 2 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } < 13$
$2 x \color{#FF6800}{ - } \color{#FF6800}{ 2 } - 5 x < 13$
 Move the constant to the right side and change the sign 
$2 x - 5 x < 13 \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } < 13 + 2$
 Organize the expression 
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } < 13 + 2$
$- 3 x < \color{#FF6800}{ 13 } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
 Add $13$ and $2$
$- 3 x < \color{#FF6800}{ 15 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } < \color{#FF6800}{ 15 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$3 x > - 15$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 15 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
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Inequality
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