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Solve an expression involving the absolute value
Answer
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Graph
$| 7 - x | > 0$
$| 7 - x | > 0$
Solution of inequality
$x < 7 \text{ or } x > 7$
$x < 7 $ or $ x > 7$
$ $ Solve a solution to $ x$
$| \color{#FF6800}{ 7 } \color{#FF6800}{ - } \color{#FF6800}{ x } | > 0$
$ $ Organize the expression $ $
$| \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } | > 0$
$| \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } | > \color{#FF6800}{ 0 }$
$ $ Divide the interval based on the value where the inside of the absolute value is 0 $ $
$\color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } > \color{#FF6800}{ 0 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 7 } \right ) \\ \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \right ) > \color{#FF6800}{ 0 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 7 } \right )$
$\color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } > \color{#FF6800}{ 0 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 7 } \right ) \\ \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \right ) > \color{#FF6800}{ 0 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 7 } \right )$
$ $ Find the solution $ $
$\color{#FF6800}{ x } < \color{#FF6800}{ 7 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 7 } \right ) \\ \color{#FF6800}{ x } > \color{#FF6800}{ 7 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 7 } \right )$
$\color{#FF6800}{ x } < \color{#FF6800}{ 7 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 7 } \right ) \\ \color{#FF6800}{ x } > \color{#FF6800}{ 7 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 7 } \right )$
$ $ Make sure if the value is within the interval $ $
$\color{#FF6800}{ x } < \color{#FF6800}{ 7 } \\ \color{#FF6800}{ x } > \color{#FF6800}{ 7 }$
$\color{#FF6800}{ x } < \color{#FF6800}{ 7 } \\ \color{#FF6800}{ x } > \color{#FF6800}{ 7 }$
$ $ Find the union of sets of each interval $ $
$\color{#FF6800}{ x } < \color{#FF6800}{ 7 } $ or $ \color{#FF6800}{ x } > \color{#FF6800}{ 7 }$
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