Question

The number line below represents which combined inequality? number line with a closed circle on -4, shading to the left and a closed circle on 3, shading to the right x greater than or equal to -4 and x less than or greater to 3 x greater than or equal to -4 or x less than or greater to 3 x less than or greater to -4 and x greater than or equal to 3 x less than or greater to -4 or x greater than or equal to 3

Answer 1

It is stated that their are closed circles on -4 and 3. This means, both -4 and 3 are also included in the interval.

The following regions are included in the range:

a) -4 
b) Numbers between -4 and 3
c) 3
d) Numbers greater than 3

So, the number line represents:
x greater than or equal to -4 and x less than or greater to 3.

Therefore, the first option gives the correct combined inequality. 

Answer 2

Answer:

The combined inequality that is represented by the number line is:

      x less than or equal to -4 or x greater than or equal to 3

Step-by-step explanation:

• Number line with a closed circle on -4, shading to the left .

This means that the inequality that is satisfied is:

                      x ≤ -4

Since, shaded region to left means that all the values less than that number are covered.

Also, closed circle at a number means that that number is also included in the range and hence, the inequality will be a inequality with a equal sign.

• closed circle on 3, shading to the right

This means that the inequality is:

                     x ≥ 3

( Since, the shading is to the right this means that all the values greater than that number is covered.

Also, closed circle at that point means that the inequality will be a inequality with a equal sign)