Question - Solving Absolute Value Inequalities
Solution:
To solve the inequality |c| - 1 ≥ 11, follow these steps:1. Start by isolating the absolute value on one side of the inequality: |c| - 1 + 1 ≥ 11 + 1 |c| ≥ 122. Next, understand that an absolute value being greater than or equal to a positive number means the expression inside the absolute value can be either greater than or equal to that number or less than or equal to the negative of that number. In other words, if |a| ≥ b and b > 0, then a ≥ b or a ≤ -b.So for |c| ≥ 12, we have two cases: Case 1: c ≥ 12 Case 2: c ≤ -12The solution to the inequality |c| - 1 ≥ 11 is therefore all c that are greater than or equal to 12, combined with all c that are less than or equal to -12. This can be expressed as: c ≥ 12 or c ≤ -12Or, in interval notation: c ∈ (-∞, -12] ∪ [12, ∞)
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