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Solve an expression involving the absolute value

Answer

Graph

$| x - 2 | < 2$

Solution of inequality

$0 < x < 4$

$ $ 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 $ $

$\color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) < \color{#FF6800}{ 2 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } < \color{#FF6800}{ 2 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 2 } \right )$

$ $ Find the solution $ $

$\color{#FF6800}{ x } > \color{#FF6800}{ 0 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 2 } \right ) \\ \color{#FF6800}{ x } < \color{#FF6800}{ 4 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 2 } \right )$

$ $ Make sure if the value is within the interval $ $

$\color{#FF6800}{ 0 } < \color{#FF6800}{ x } < \color{#FF6800}{ 2 } \\ \color{#FF6800}{ 2 } \leq \color{#FF6800}{ x } < \color{#FF6800}{ 4 }$

$ $ Find the union of sets of each interval $ $

$\color{#FF6800}{ 0 } < \color{#FF6800}{ x } < \color{#FF6800}{ 4 }$

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