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Solve the inequality
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Graph
$0.5 \left ( x - 2 \right ) \leq 0.7 x - 1.2$
$0.5 \left ( x - 2 \right ) \leq 0.7 x - 1.2$
Solution of inequality
$x \geq 1$
$x \geq 1$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 0.5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \leq 0.7 x - 1.2$
$ $ Multiply each term in parentheses by $ 0.5$
$\color{#FF6800}{ 0.5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 0.5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \leq 0.7 x - 1.2$
$\color{#FF6800}{ 0.5 } \color{#FF6800}{ x } + 0.5 \times \left ( - 2 \right ) \leq 0.7 x - 1.2$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } + 0.5 \times \left ( - 2 \right ) \leq 0.7 x - 1.2$
$\dfrac { x } { 2 } + \color{#FF6800}{ 0.5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \leq 0.7 x - 1.2$
$ $ Multiply $ 0.5 $ and $ - 2$
$\dfrac { x } { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \leq 0.7 x - 1.2$
$\dfrac { x } { 2 } - 1 \leq \color{#FF6800}{ 0.7 } \color{#FF6800}{ x } - 1.2$
$ $ Calculate the multiplication expression $ $
$\dfrac { x } { 2 } - 1 \leq \color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } } - 1.2$
$\dfrac { x } { 2 } - 1 \leq \dfrac { 7 x } { 10 } \color{#FF6800}{ - } \color{#FF6800}{ 1.2 }$
$ $ Convert decimals to fractions $ $
$\dfrac { x } { 2 } - 1 \leq \dfrac { 7 x } { 10 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 6 } } { \color{#FF6800}{ 5 } } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \leq \color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 6 } } { \color{#FF6800}{ 5 } } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 10 } \leq \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 12 }$
$5 x - 10 \leq \color{#FF6800}{ 7 } \color{#FF6800}{ x } - 12$
$ $ Move the variable to the left-hand side and change the symbol $ $
$5 x - 10 \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \leq - 12$
$5 x \color{#FF6800}{ - } \color{#FF6800}{ 10 } - 7 x \leq - 12$
$ $ Move the constant to the right side and change the sign $ $
$5 x - 7 x \leq - 12 \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \leq - 12 + 10$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \leq - 12 + 10$
$- 2 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 12 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$ $ Add $ - 12 $ and $ 10$
$- 2 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$ $ Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction $ $
$2 x \geq 2$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq \color{#FF6800}{ 2 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } \geq \color{#FF6800}{ 1 }$
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