Question

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

Answer 1

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

Answer 2

it comes out the same

Answer 3

2x+6 is greater than or equal to 8

Answer 4

but then I get stuck from there

Answer 5

\[
|x| = \left\{
\begin{array}{lr}
x & : x \ge 0 \\
-x & : x < 0
\end{array}
\right.
\]

so if
\[ \large |2x+6| \ge 8 \]
\[ \Leftrightarrow -\left(2x+6\right) \ge 8 \Leftrightarrow \left(2x+6\right) \ge -8 \] or \[ \Leftrightarrow \left(2x+6\right) \ge 8 \]

Answer 6

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