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Solve the inequality
Answer
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Graph
$0.5 x + 1.6 \leq 0.3 x$
$0.5 x + 1.6 \leq 0.3 x$
Solution of inequality
$x \leq - 8$
$0.5x+1.6 \leq 0.3x$
$x \leq - 8$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 0.5 } \color{#FF6800}{ x } + 1.6 \leq 0.3 x$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { x } { 2 } } + 1.6 \leq 0.3 x$
$\dfrac { x } { 2 } + \color{#FF6800}{ 1.6 } \leq 0.3 x$
$ $ Convert decimals to fractions $ $
$\dfrac { x } { 2 } + \color{#FF6800}{ \dfrac { 8 } { 5 } } \leq 0.3 x$
$\dfrac { x } { 2 } + \dfrac { 8 } { 5 } \leq \color{#FF6800}{ 0.3 } \color{#FF6800}{ x }$
$ $ Calculate the multiplication expression $ $
$\dfrac { x } { 2 } + \dfrac { 8 } { 5 } \leq \color{#FF6800}{ \dfrac { 3 x } { 10 } }$
$\color{#FF6800}{ \dfrac { x } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 8 } { 5 } } \leq \color{#FF6800}{ \dfrac { 3 x } { 10 } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 16 } \leq \color{#FF6800}{ 3 } \color{#FF6800}{ x }$
$5 x + 16 \leq \color{#FF6800}{ 3 } \color{#FF6800}{ x }$
$ $ Move the variable to the left-hand side and change the symbol $ $
$5 x + 16 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \leq 0$
$5 x \color{#FF6800}{ + } \color{#FF6800}{ 16 } - 3 x \leq 0$
$ $ Move the constant to the right side and change the sign $ $
$5 x - 3 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 16 }$
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \leq - 16$
$ $ Organize the expression $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \leq - 16$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ 16 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
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