Answer:
6. x < -5 and x > 2
7. -5 < x < 2
Explanation:
If the circle open, (think O shaped) then the inequality doesn't include that number it is over. If the circle is closed, (think solid black circle) than the number is included in the inequality. Arrows pointing to the right include all numbers greater than the dot, pointing to the left includes all numbers less than where the dot is.
6. We have two open circles. So our inequality symbols will use < and >, not ≤ or ≥. The first of the two arrows starts -5 with an open circle and points to the left, representing all numbers less than -5. So the inequality for that arrow is x < -5. The second arrow shows an open circle at 2 pointing to the right. This represents all numbers greater than 2, excluding 2 itself. So the matching inequality would be x > 2. We put these two inequalities together such that x < -5 and x > 2.
7. We have a single segment that spans -5 to 2 with open circles. This means that the inequality represents values in between -5 and 2, excluding those endpoints. So -4.9999 is included and so is 1.999, but not -5 or 2. The inequality that represents this situtation would be -5 < x < 2.
Any of the mentioned inequalities can be used with a variable of your choosing. (I'm using x as an example)