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Absolute Value

For a real number, the absolute value of \(x\), denoted \( \lvert x \rvert \), is defined as

\[ \left|x \right| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0. \end{cases} \]

Working with absolute value often requires dealing with each of these cases separately. This can be clearly seen in the graph of the absolute value function \( y = \lvert x \rvert \), where the slope of the line is 1 when \( x > 0\) but is -1 when \( x < 0 \).

For example, to evaluate \( \left| 3\left( 17-55 \right) \right| \):

\[ \begin{align} \left| 3\left( 17-55 \right) \right| &= \left| 3\left( -38 \right) \right| \\ &= \left| -114 \right| \\ &= 114. \end{align} \]

Note by Arron Kau
3 years, 2 months ago

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