03 - Describe the set S = ½x − 3 in terms of intervals.​

Question

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

Answer 1

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)\\`