To calculate: The solution of absolute value inequality −9≤4−|2k−1| and write solution set in interval notation.

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delilnaT · Accepted Answer

Step 1  Consider the provided absolute inequality −9≤4−|2k−1|  First iosolate the absolute value. Subtract 4 from all two parts of the inequality.  −9−4≤4−4−|2k−1|  −13≤−|2k−1|  13≥|2k−1|  |2k−1|≤13  The inequality is in the form |u|≤k, where u=2k−1 Write the equivalent compound inequality −k≤u≤k  −13≤2k−1≤13  Add 1 to all the three partss in the equality.  −13+1≤2k−1+1≤13+1  −12≤2k≤14  Divide 2 from all the three parts in the equality  −122≤2k2≤142  −6≤k≤7  Therefore, the solution set is {x∣−6≤k≤7} and the solution in interval notation is [−6, 7]

To calculate: The solution of absolute value inequality -9\leq4-|2k-1| and

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