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Formula
Solve an expression involving the absolute value
Answer
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Graph
$| x - 2 | < 2$
$| x - 2 | < 2$
Solution of inequality
$0 < x < 4$
$| x-2 | < 2$
$0 < x < 4$
$ $ Solve a solution to $ x$
$| \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } | < \color{#FF6800}{ 2 }$
$ $ Divide the interval based on the value where the inside of the absolute value is 0 $ $
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) < \color{#FF6800}{ 2 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } < \color{#FF6800}{ 2 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 2 } \right )$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) < \color{#FF6800}{ 2 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } < \color{#FF6800}{ 2 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 2 } \right )$
$ $ Find the solution $ $
$\color{#FF6800}{ x } > \color{#FF6800}{ 0 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ x } < \color{#FF6800}{ 4 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 2 } \right )$
$\color{#FF6800}{ x } > \color{#FF6800}{ 0 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ x } < \color{#FF6800}{ 4 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 2 } \right )$
$ $ Make sure if the value is within the interval $ $
$\color{#FF6800}{ 0 } < \color{#FF6800}{ x } < \color{#FF6800}{ 2 } \\ \color{#FF6800}{ 2 } \leq \color{#FF6800}{ x } < \color{#FF6800}{ 4 }$
$\color{#FF6800}{ 0 } < \color{#FF6800}{ x } < \color{#FF6800}{ 2 } \\ \color{#FF6800}{ 2 } \leq \color{#FF6800}{ x } < \color{#FF6800}{ 4 }$
$ $ Find the union of sets of each interval $ $
$\color{#FF6800}{ 0 } < \color{#FF6800}{ x } < \color{#FF6800}{ 4 }$
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