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In the following inequality, x ≥ −2, what type of circle would appear on the number line (open or closed circle) and in which direction would the arrow point on the number line(right or left)?

Also, what is a possible solution to x ≥ −2?

Please answer all of the questions in sentence form.
(10 Points)

Answer:

A closed circle would appear on the number line and the arrow should be pointing towards right. The possible solutions could be basically anything greater than or equal to -2, it could be -2, -1, 0, 1, 2, 3, 4 and so on.

Step-by-step explanation:

There are a few things to consider:

1. The inequality symbol:

⇒      [tex]\leq or \geq[/tex] always represented by a closed circle on the number line (this also means that the function x ≥ −2 would contain values greater than -2 but it WOULD also include -2 as an answer, but anything less than -2 would not be included).

⇒      < or > always represented by an open circle on the number line (This also means that the function would contain all numbers greater than -2 but NOT -2 or anything greater).

2. Where the Inequality sign opens:

⇒      If the inequality sign opens towards the variable (a letter) it means that all the values will be greater than the value given in the function. (For example x > 2, since the inequality sign is opening towards the x it means that all values in the solution set would be greater than two and thus the arrow would face the right side. The possible solution set could be 3, 4, 5 and so on)

⇒       If the inequality sign opens towards the number value given, it means that all the values will be less than the value given in the function. (For example, x < 2, in this case the inequality faces towards the number value given so the values for the answer set will have every value less than 2, the solution set would contain values like 1, 0, -1, and so on).

Hope this helps! Good Luck! I'd appreciate if I got Brainliest :) Have a good day!

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