Answer :
Answer:
Option 1
Step-by-step explanation:
[tex]|x-2|<14 \\ \\ x-2<-14, x-2>14 \\ \\ x<-12, x>16[/tex]
Final answer:
To find the solution to the inequality |x – 2| + 3 > 17, isolate the absolute value and consider two cases: x - 2 > 0 and x - 2 < 0. Solve for x in each case and combine the solutions.
Explanation:
To find the solution to the inequality |x – 2| + 3 > 17, we first need to isolate the absolute value. We subtract 3 from both sides to get |x - 2| > 14. Then, we have two cases to consider. Case 1: x - 2 > 0. In this case, we solve x - 2 > 14, which gives us x > 16. Case 2: x - 2 < 0. Here, we solve -(x - 2) > 14, which simplifies to -x + 2 > 14. Solving for x, we find x < -12. Putting both cases together, the solution is x < -12 or x > 16.
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