Question

ASAP can somebody answer this? SCREEN SHOT OF QUESTION ATTACHED

Answer 1

Answer:

A. $(-\infty, -4]\ or\ (2,\infty)$

Step-by-step explanation:

Given:

The inequality is given as:

$x\leq-4\ or\ x>2$

Now, consider the first inequality

$x\leq-4$

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, $(-\infty,-4]$

Now, consider the other inequality $x>2$

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, $x>2$ in interval notation form is $(2,\infty)$

There is a conjunction 'or' used in the inequality. Therefore, the answer is:

A. $(-\infty, -4]\ or\ (2,\infty)$

The graph on the number line is shown below.