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Solve the inequality

Answer

Graph

$\dfrac { 1 } { 4 } x + 0.6 \geq 0.2 x - \dfrac { 1 } { 5 }$

Solution of inequality

$x \geq - 16$

$ $ Solve a solution to $ x$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 4 } } } \color{#FF6800}{ x } + 0.6 \geq 0.2 x - \dfrac { 1 } { 5 }$

$ $ Calculate the multiplication expression $ $

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 4 } } } + 0.6 \geq 0.2 x - \dfrac { 1 } { 5 }$

$\dfrac { x } { 4 } + \color{#FF6800}{ 0.6 } \geq 0.2 x - \dfrac { 1 } { 5 }$

$ $ Convert decimals to fractions $ $

$\dfrac { x } { 4 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 5 } } } \geq 0.2 x - \dfrac { 1 } { 5 }$

$\dfrac { x } { 4 } + \dfrac { 3 } { 5 } \geq \color{#FF6800}{ 0.2 } \color{#FF6800}{ x } - \dfrac { 1 } { 5 }$

$ $ Calculate the multiplication expression $ $

$\dfrac { x } { 4 } + \dfrac { 3 } { 5 } \geq \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 5 } } } - \dfrac { 1 } { 5 }$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 4 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 5 } } } \geq \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 5 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 5 } } }$

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

$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \geq \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 }$

$5 x + 12 \geq \color{#FF6800}{ 4 } \color{#FF6800}{ x } - 4$

$ $ Move the variable to the left-hand side and change the symbol $ $

$5 x + 12 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \geq - 4$

$5 x \color{#FF6800}{ + } \color{#FF6800}{ 12 } - 4 x \geq - 4$

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

$5 x - 4 x \geq - 4 \color{#FF6800}{ - } \color{#FF6800}{ 12 }$

$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \geq - 4 - 12$

$ $ Organize the expression $ $

$\color{#FF6800}{ x } \geq - 4 - 12$

$x \geq \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 12 }$

$ $ Find the sum of the negative numbers $ $

$x \geq \color{#FF6800}{ - } \color{#FF6800}{ 16 }$