@friedch1cken 4x 15 A number line with a closed circle on -4, shading to the left, and an open circle on 10, shading to the right. A number line with an open circle on -4, a closed circle on 10, and shading in between. A number line with a closed circle on -4, an open circle on 10, and shading in between. A number line with an open circle on -4, shading to the left, and a closed circle on 10, shading to the right.

Question

@friedch1cken
4x < -16 or x + 5 =>  15

A number line with a closed circle on -4, shading to the left, and an open circle on 10, shading to the right.

A number line with an open circle on -4, a closed circle on 10, and shading in between.

A number line with a closed circle on -4, an open circle on 10, and shading in between.

A number line with an open circle on -4, shading to the left, and a closed circle on 10, shading to the right.

anonymous · Answer

Okay, so you have your first inequality
4x < -16. We need to solve it for x. In order to do that, we divide both sides of the equation by 4. By doing that we get
x < -4

The next inequality is x  + 5 =>  15 
In order to solve this one for x, we need to subtract 5 from both sides. In doing this, we get
$$x \ge 10$$

Since your first inequality is less than and not equal to, we can use a closed circle on 4. Since the second inequality is greater than or equal to, we can use an open circle on 10. That narrows it down to the 1st or 3rd answer.
Since the first inequality is pointing left, we draw the arrow left. The second inequality is pointing right; we draw the arrow right. 

So, your answer would be the 1st one, a number line with a closed circle on -4, shading to the left, and an open circle on 10, shading to the right.