Final answer:
To solve the inequality [2+2w]-4>6, subtract 4 from both sides and remove the absolute value brackets by considering two cases. The solution in set notation is w > 4 or w < -6.
Step-by-step explanation:
To solve the inequality [2+2w]-4>6, we can start by subtracting 4 from both sides of the inequality:
[2+2w]-4-4 > 6-4
This simplifies to:
[2+2w] > 10
Next, we can remove the absolute value brackets by considering two cases:
Case 1: If 2+2w is positive, we simply have 2+2w > 10. Solving this inequality gives:
2+2w > 10
2w > 8
w > 4
Case 2: If 2+2w is negative, we have -(2+2w) > 10. Solving this inequality gives:
-2-2w > 10
-2w > 12
w < -6
Combining the solutions from both cases, the solution in set notation is:
w