To solve the inequality \(|2x - 6| \geq 9\), we will break it down into two cases.
Case 1:
\(2x - 6 \geq 9\)
Add 6 to both sides: \[ 2x \geq 15 \] Divide both sides by 2: \[ x \geq 7.5 \]
Case 2:
\(2x - 6 \leq -9\)
Add 6 to both sides: \[ 2x \leq -3 \] Divide both sides by 2: \[ x \leq -1.5 \]
Thus, combining the two cases, we have: \[ x \leq -1.5 \quad \text{or} \quad x \geq 7.5 \]
In interval notation, the solution is: \[ (-\infty, -1.5] \cup [7.5, \infty) \]
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