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Solve the inequality
Answer
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Graph
$0.1 \left ( x - 7 \right ) < - 0.2 x - 1$
$0.1 \left ( x - 7 \right ) < - 0.2 x - 1$
Solution of inequality
$x < - 1$
$0.1 \left( x-7 \right) < -0.2x-1$
$x < - 1$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 0.1 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 7 } \right ) < - 0.2 x - 1$
$ $ Multiply each term in parentheses by $ 0.1$
$\color{#FF6800}{ 0.1 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 0.1 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \right ) < - 0.2 x - 1$
$\color{#FF6800}{ 0.1 } \color{#FF6800}{ x } + 0.1 \times \left ( - 7 \right ) < - 0.2 x - 1$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { x } { 10 } } + 0.1 \times \left ( - 7 \right ) < - 0.2 x - 1$
$\dfrac { x } { 10 } + \color{#FF6800}{ 0.1 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 7 } \right ) < - 0.2 x - 1$
$ $ Multiply $ 0.1 $ and $ - 7$
$\dfrac { x } { 10 } \color{#FF6800}{ - } \color{#FF6800}{ 0.7 } < - 0.2 x - 1$
$\dfrac { x } { 10 } \color{#FF6800}{ - } \color{#FF6800}{ 0.7 } < - 0.2 x - 1$
$ $ Convert decimals to fractions $ $
$\dfrac { x } { 10 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 10 } } < - 0.2 x - 1$
$\dfrac { x } { 10 } - \dfrac { 7 } { 10 } < \color{#FF6800}{ - } \color{#FF6800}{ 0.2 } \color{#FF6800}{ x } - 1$
$ $ Calculate the multiplication expression $ $
$\dfrac { x } { 10 } - \dfrac { 7 } { 10 } < \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 5 } } - 1$
$\color{#FF6800}{ \dfrac { x } { 10 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 10 } } < \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 7 } < \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 10 }$
$x - 7 < \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } - 10$
$ $ Move the variable to the left-hand side and change the symbol $ $
$x - 7 \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } < - 10$
$x \color{#FF6800}{ - } \color{#FF6800}{ 7 } + 2 x < - 10$
$ $ Move the constant to the right side and change the sign $ $
$x + 2 x < - 10 \color{#FF6800}{ + } \color{#FF6800}{ 7 }$
$\color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } < - 10 + 7$
$ $ Organize the expression $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } < - 10 + 7$
$3 x < \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ + } \color{#FF6800}{ 7 }$
$ $ Add $ - 10 $ and $ 7$
$3 x < \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } < \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } < \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
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