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Solve the inequality
Answer
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Graph
$0.3 x - 4 \geq 0.25 \left ( x - 10 \right )$
$0.3 x - 4 \geq 0.25 \left ( x - 10 \right )$
Solution of inequality
$x \geq 30$
$x \geq 30$
$ $ Solve a solution to $ x$
$0.3 x - 4 \geq \color{#FF6800}{ 0.25 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 10 } \right )$
$ $ Multiply each term in parentheses by $ 0.25$
$0.3 x - 4 \geq \color{#FF6800}{ 0.25 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 0.25 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 10 } \right )$
$\color{#FF6800}{ 0.3 } \color{#FF6800}{ x } - 4 \geq 0.25 x + 0.25 \times \left ( - 10 \right )$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } } - 4 \geq 0.25 x + 0.25 \times \left ( - 10 \right )$
$\dfrac { 3 x } { 10 } - 4 \geq \color{#FF6800}{ 0.25 } \color{#FF6800}{ x } + 0.25 \times \left ( - 10 \right )$
$ $ Calculate the multiplication expression $ $
$\dfrac { 3 x } { 10 } - 4 \geq \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 4 } } } + 0.25 \times \left ( - 10 \right )$
$\dfrac { 3 x } { 10 } - 4 \geq \dfrac { x } { 4 } + \color{#FF6800}{ 0.25 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 10 } \right )$
$ $ Multiply $ 0.25 $ and $ - 10$
$\dfrac { 3 x } { 10 } - 4 \geq \dfrac { x } { 4 } \color{#FF6800}{ - } \color{#FF6800}{ 2.5 }$
$\dfrac { 3 x } { 10 } - 4 \geq \dfrac { x } { 4 } \color{#FF6800}{ - } \color{#FF6800}{ 2.5 }$
$ $ Convert decimals to fractions $ $
$\dfrac { 3 x } { 10 } - 4 \geq \dfrac { x } { 4 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \geq \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 4 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 2 } } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 80 } \geq \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 50 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) - 80 \geq 5 x - 50$
$ $ Get rid of unnecessary parentheses $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ x } - 80 \geq 5 x - 50$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ x } - 80 \geq 5 x - 50$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 6 } \color{#FF6800}{ x } - 80 \geq 5 x - 50$
$6 x - 80 \geq \color{#FF6800}{ 5 } \color{#FF6800}{ x } - 50$
$ $ Move the variable to the left-hand side and change the symbol $ $
$6 x - 80 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \geq - 50$
$6 x \color{#FF6800}{ - } \color{#FF6800}{ 80 } - 5 x \geq - 50$
$ $ Move the constant to the right side and change the sign $ $
$6 x - 5 x \geq - 50 \color{#FF6800}{ + } \color{#FF6800}{ 80 }$
$\color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \geq - 50 + 80$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } \geq - 50 + 80$
$x \geq \color{#FF6800}{ - } \color{#FF6800}{ 50 } \color{#FF6800}{ + } \color{#FF6800}{ 80 }$
$ $ Add $ - 50 $ and $ 80$
$x \geq \color{#FF6800}{ 30 }$
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