Answer:
Interval notation: [tex](-\infty,5) \cup (5, \infty)[/tex]
Step-by-step explanation:
If x includes all other numbers except 5, then we need to use parenthesis for interval notation, parenthesis notation excludes the values, while brackets are mostly used when we are including the number.
Setting up the intervals
If we do not include just one single number 5, we need to include all other real numbers before 5, and all real numbers after 5, that is why we need to use 2 sets to describe [tex]x \ne 5[/tex].
Before 5, we can write the interval,
[tex](-\infty, 5)[/tex]
This interval includes all real numbers from -infinity to 5, but not including either the -infinity or the 5.
After 5 we can write the interval,
[tex](5, \infty)[/tex]
This interval includes all real numbers from 5 to infinity, but not including either 5 or infinity.
Lastly we can join both intervals into one single answer using union U or a comma.
[tex](-\infty,5) \cup (5, \infty)[/tex]
This is the answer on interval notation.
Notice as well that in some textbooks they use brackets only but on the opposite direction ][ to denote exclusion and [ ] to denote inclusion, so the answer [tex]]-\infty, 5[\cup ]5, \infty[[/tex] is valid as well, it is just not that common.
Writing in interval notation, the answer is:
[tex](-\infty, \infty) - \{5\}[/tex]
----------------------------------------
In interval notation, all real numbers for x are represented by:
[tex](-\infty, \infty)[/tex]
We want to remove only one of the values, which is 5. Thus, the number 5 has to be subtracted from the interval, which is done as follows:
[tex](-\infty, \infty) - \{5\}[/tex]
Which is the desired interval.
A similar problem is given at https://brainly.com/question/10906966
