Question - Solving Absolute Value Inequalities
Solution:
Certainly! We have an inequality involving an absolute value: |u - 7| > 29.Recall that |x| > a, where a is a positive number, implies two situations:1. x > a2. x < -aApplying this to our inequality, we split it into two separate inequalities:u - 7 > 29 and u - 7 < -29For the first inequality (u - 7 > 29), we solve for u by adding 7 to both sides:u > 29 + 7u > 36For the second inequality (u - 7 < -29), we again solve for u by adding 7 to both sides:u < -29 + 7u < -22Therefore, the solutions to the inequality |u - 7| > 29 are:u > 36 or u < -22These inequalities represent the range of values that u can take to satisfy the original inequality.
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