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Need a little help understanding this one. Solve the absolute value inequality. |2x + 6| ≥ 8
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can you tell me what do you know about absolute value? :)
it comes out the same
2x+6 is greater than or equal to 8
but then I get stuck from there
\[ |x| = \left\{ \begin{array}{lr} x & : x \ge 0 \\ -x & : x < 0 \end{array} \right. \] so if \[ \large |2x+6| \ge 8 \] \[ \Leftrightarrow -\left(2x+6\right) \ge 8 \Leftrightarrow \left(2x+6\right) \ge -8 \] or \[ \Leftrightarrow \left(2x+6\right) \ge 8 \]
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in general if \[ |x| < a \Leftrightarrow -a<x<a \] \( |x| >a \Leftrightarrow x<-a\) or \(x>a\)
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