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Grade 11Algebra

Please answer the question attached in image.
The answer is (-infinity,-17] U [17,infinity)

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7 Years agoGrade 11
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ApprovedApproved Tutor Answer7 Years ago
it is obvious that |[|x|-5]| – 11 should be greater than zero
or |[|x|-5]| should be greater than 11
or [|x|-5] should lie in (-inf,-11)U(11,inf)
or |x|-5 should lie in (-inf, -11)U[12, inf).
or |x| should lie in (-inf, -6)U[17, inf).
but |x| cant lie in (-inf, -6)
so it has to lie in [17, inf).
or x belongs to (-infinity,-17] U [17,infinity)