Question

How would I mark the numberline?

Answer 1

Answer:

-4 < x ≤ 1.5

Step-by-step explanation:

First we will need to determine what signs to use for our inequality:

• An open circle represents either greater than (>) or less than (<)
• A closed circle represents either greater than or equal to (≥) or less than or equal to (≤)

According to the picture, we have one of each

• The point on -4 will be either > or <
• The point on 1.5 or 3/2 will be ≥ or ≤  

So we need to write an equality for each point and then combine them

• The sign of the inequality will "point" in the direction of the shaded line as long as the variable is on the left side of the inequality

The first inequality will be x > -4 because here the shading is "pointing" to the right just as the inequality sign >

The second inequality will be x ≤ 1.5 because here the shading is "pointing" to the left just as the inequality sign ≤

Now to combine, we arrange the two number values that we have from least to greatest with the smallest number being on the leftmost side of the inequality and the larger number being on the rightmost side of the inequality.

• So here -4 will be on the left and 1.5 will be on the right

Then we put x in the middle and add the signs that we have

• Keep in mind, your "smaller numbered inequality" sign will be "flipped" because it will read backwards, but it is still equivalent to the same thing

So our complete inequality will read -4 < x ≤ 1.5