Question

Can you please help and explain?Which of the following compound inequalities is shown graphically?

Answer 1

The first arrow is pointing to the left, that means that all the numbers below -1 are considered. Note also that in the number -1 the circle is empty, so this represents that this number does not satisfy the inequality. This considerations are represented in the following way

`x<-1`

Then, since the other arrow starts at 5 and points to the right, all the numbers above 5 are considered, including 5 itself. This is represented by the inequality

`x\ge5`

Since either the number is less than -1 or is greater or equal than 5, then the inequalities that we have to choose is

`x<-1\text{ or x}\ge5`

This compound inequality is the number (3).