8) 3 + | - 6n | ≥ 33
8) 3 + | - 6n | ≥ 33
Answer
Explanation:
Step1: Isolate the absolute value expression
Subtract (3) from both sides of the inequality (3+\vert - 6n\vert\geq33). (3+\vert - 6n\vert-3\geq33 - 3) (\vert - 6n\vert\geq30) Since (\vert - 6n\vert=\vert6n\vert) (because (\vert a\vert=\vert - a\vert) for any real number (a)), the inequality becomes (\vert6n\vert\geq30).
Step2: Solve the absolute - value inequality
Recall that if (\vert x\vert\geq k) ((k\geq0)), then (x\geq k) or (x\leq - k). For (\vert6n\vert\geq30), we have two cases:
- Case 1: (6n\geq30) Divide both sides by (6): (n\geq\frac{30}{6}=5)
- Case 2: (6n\leq - 30) Divide both sides by (6): (n\leq\frac{-30}{6}=- 5)
Answer:
(n\leq - 5) or (n\geq5)