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Mathematics
OpenStudy (anonymous):

Need a little help understanding this one. Solve the absolute value inequality. |2x + 6| ≥ 8

OpenStudy (chihiroasleaf):

can you tell me what do you know about absolute value? :)

OpenStudy (anonymous):

it comes out the same

OpenStudy (anonymous):

2x+6 is greater than or equal to 8

OpenStudy (anonymous):

but then I get stuck from there

OpenStudy (chihiroasleaf):

\[ |x| = \left\{ \begin{array}{lr} x & : x \ge 0 \\ -x & : x < 0 \end{array} \right. \] so if \[ \large |2x+6| \ge 8 \] \[ \Leftrightarrow -\left(2x+6\right) \ge 8 \Leftrightarrow \left(2x+6\right) \ge -8 \] or \[ \Leftrightarrow \left(2x+6\right) \ge 8 \]

OpenStudy (chihiroasleaf):

in general if \[ |x| < a \Leftrightarrow -a<x<a \] \( |x| >a \Leftrightarrow x<-a\) or \(x>a\)

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