Question

Please help me and I will give the pictures for the choices..

Answer 1

The first compound indequality is:

`x>7\, and\, x<7`

We can view this in the real line:

There is no number that can be both greater AND less than 7, which makes the correct answer "No solution".

The second is:

`x<7\, or\, x>7`

Now, we are not looking for intercetion, we are looking for the union of both. The firts inequality takes all number less than 7 and the second all that are greater than 7, so the only one that is not a solution is 7, which means the correct answer is "all real numbers except 7"

The third is:

`x\ge7\, and\, x\le7`

This is the same as the first one, but now the 7 is included in both:

So, there is only 7 that can be in both indequalitys, thus the correct answer is "one solution, 7".

The fourth is

`x\le7\, or\, x\ge7`

This is similar to the second, but now 7 is included, which means it is also a solution, thus the answer is "all real numbers".