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03 - Describe the set S = x : in terms of intervals.​

1 Answer

1 vote

Answer:

Hi,

Explanation:

a)


if\ (x)/(2)-3\ > \ 0\ then\ |(x)/(2)-3|=(x)/(2)-3\\\\(x)/(2)-3 > 4\\\\(x)/(2) > 7\\\\x > 14\\

b)


if\ (x)/(2)-3\ < \0 \ then\ |(x)/(2)-3|=-((x)/(2)-3)=-(x)/(2)+3\\\\-(x)/(2)+3\ > \ 4\\\\-(x)/(2)\ > \ 4-3\\\\-(x)/(2)\ > \ 1\\\\(x)/(2)\ < \ -1\\\\x\ < \ -2\\


S=\{x\in\mathbb{R}\ :\ |(x)/(2)-3|\ > \ 4\}=(-\infty,-2[\ \cup\ ]14,\infty)\\

User Elliott Hughes
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