Answer:
A. [tex](-\infty, -4]\ or\ (2,\infty)[/tex]
Step-by-step explanation:
Given:
The inequality is given as:
[tex]x\leq-4\ or\ x>2[/tex]
Now, consider the first inequality
[tex]x\leq-4[/tex]
Here, 'x' is less than or equal to -4. The values that are less than -4 are -5, -6, -7... so on. The inequality used is 'less than or equal to'. This means that -4 is included in the solution. So, we use a square bracket (closed interval) at the other end.
The inequality in notation form is thus, [tex](-\infty,-4][/tex]
Now, consider the other inequality [tex]x>2[/tex]
The values of 'x' are greater than 2. The values that are greater than 2 are 3, 4, 5... and so on. Also, 2 is not included in the solution. So, we use open interval on either side.
Therefore, [tex]x>2[/tex] in interval notation form is [tex](2,\infty)[/tex]
There is a conjunction 'or' used in the inequality. Therefore, the answer is:
A. [tex](-\infty, -4]\ or\ (2,\infty)[/tex]
The graph on the number line is shown below.
