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Kpress your answer in interval notation. 6-|(x)/(2)+4|>=11

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Final answer:

The inequality 6 - |(x)/(2) + 4| ≥ 11 has no solution because an absolute value cannot be less than a negative number. Therefore, the solution in interval notation is expressed as an empty set, ∅.

Step-by-step explanation:

The question involves solving an inequality and expressing the solution in interval notation. To solve the inequality 6 - |(x)/(2) + 4| ≥ 11, we first isolate the absolute value expression by subtracting 6 from both sides to get -|(x)/(2) + 4| ≥ 5.

Next, we divide both sides by -1, remembering that this will reverse the inequality sign, resulting in |(x)/(2) + 4| ≤ -5. However, since an absolute value cannot be less than a negative number, this inequality has no solution.

Therefore, there are no values of x that satisfy the original inequality, and the solution set is empty. The interval notation for an empty set is () or ∅.

User Marcel Hofgesang
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