Question - Solving Inequalities with Absolute Value
Solution:
The inequality given in the image is |u + 6| ≥ 46. To solve for u, we need to consider the two scenarios that arise from the absolute value:1. When u + 6 is non-negative:u + 6 ≥ 46Subtract 6 from both sides to isolate u:u ≥ 46 - 6u ≥ 402. When u + 6 is negative:-(u + 6) ≥ 46Multiply both sides by -1, remembering to reverse the inequality sign:u + 6 ≤ -46Subtract 6 from both sides to isolate u:u ≤ -46 - 6u ≤ -52Combining both scenarios, we have a solution that u is in the interval:u ≤ -52 or u ≥ 40This means any u that is less than or equal to -52 or greater than or equal to 40 satisfies the original inequality |u + 6| ≥ 46.
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