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Solve the inequality
Answer
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Graph
$1.2 x + 0.5 \geq 0.8 x - 2.7$
$1.2 x + 0.5 \geq 0.8 x - 2.7$
Solution of inequality
$x \geq - 8$
$1.2x+0.5 \geq 0.8x-2.7$
$x \geq - 8$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 1.2 } \color{#FF6800}{ x } + 0.5 \geq 0.8 x - 2.7$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { 6 x } { 5 } } + 0.5 \geq 0.8 x - 2.7$
$\dfrac { 6 x } { 5 } + \color{#FF6800}{ 0.5 } \geq 0.8 x - 2.7$
$ $ Convert decimals to fractions $ $
$\dfrac { 6 x } { 5 } + \color{#FF6800}{ \dfrac { 1 } { 2 } } \geq 0.8 x - 2.7$
$\dfrac { 6 x } { 5 } + \dfrac { 1 } { 2 } \geq \color{#FF6800}{ 0.8 } \color{#FF6800}{ x } - 2.7$
$ $ Calculate the multiplication expression $ $
$\dfrac { 6 x } { 5 } + \dfrac { 1 } { 2 } \geq \color{#FF6800}{ \dfrac { 4 x } { 5 } } - 2.7$
$\dfrac { 6 x } { 5 } + \dfrac { 1 } { 2 } \geq \dfrac { 4 x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2.7 }$
$ $ Convert decimals to fractions $ $
$\dfrac { 6 x } { 5 } + \dfrac { 1 } { 2 } \geq \dfrac { 4 x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 27 } { 10 } }$
$\color{#FF6800}{ \dfrac { 6 x } { 5 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 2 } } \geq \color{#FF6800}{ \dfrac { 4 x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 27 } { 10 } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } } \geq \color{#FF6800}{ \dfrac { 8 x - 27 } { 2 } }$
$\color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } } \geq \color{#FF6800}{ \dfrac { 8 x - 27 } { 2 } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 12 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \geq \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 27 }$
$12 x + 5 \geq \color{#FF6800}{ 8 } \color{#FF6800}{ x } - 27$
$ $ Move the variable to the left-hand side and change the symbol $ $
$12 x + 5 \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \geq - 27$
$12 x \color{#FF6800}{ + } \color{#FF6800}{ 5 } - 8 x \geq - 27$
$ $ Move the constant to the right side and change the sign $ $
$12 x - 8 x \geq - 27 \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 12 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \geq - 27 - 5$
$ $ Organize the expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \geq - 27 - 5$
$4 x \geq \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$ $ Find the sum of the negative numbers $ $
$4 x \geq \color{#FF6800}{ - } \color{#FF6800}{ 32 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \geq \color{#FF6800}{ - } \color{#FF6800}{ 32 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } \geq \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
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