Example Question - inequality examples

Solving Inequalities with Absolute Value

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 ≥ 46 Subtract 6 from both sides to isolate u: u ≥ 46 - 6 u ≥ 40 2. When u + 6 is negative: -(u + 6) ≥ 46 Multiply both sides by -1, remembering to reverse the inequality sign: u + 6 ≤ -46 Subtract 6 from both sides to isolate u: u ≤ -46 - 6 u ≤ -52 Combining both scenarios, we have a solution that u is in the interval: u ≤ -52 or u ≥ 40 This 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.