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Question:

how do u know when to use brackets, braces or parenthesis when writing a solution in interval or set notation?

example: 3|x - 10| + 9 / 12for the answer, why do you put a parenthesis at the begining and a bracket at the end???

Answer:

parenthesis means the interval does NOT contain that number or is never ending, bracket means the interval DOES contain that number. The answer is |x - 10| / 1 or x / 11; however since there's an absolute value you can also have anything less than or equal to 11, e.g. x/11 So the answer is (-infinity, -11] and [11, +infinity) The answer INCLUDES 11 for the brackets, and for the open parenthesis, they mean infinity *if the answer were like this (-infinity, -11) and (11, +infinity), then the answer does NOT include 11*
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The parenthesis is used for greater than or less than while the bracket is used for greater than or equal to and less than or equal to.
Okay so brackets are used to show that a number cannot go past that number. Parentheses is used to show that it can go past it. Sounds confusing but here is an example. If you have x / 5, you would write (-infinity, 5]. See how since x can be less than 5, then it can be negative infinity because that is less than 5. infinity goes on forever so you use parentheses to show that it can be continuous in a negative direction. Since it cannot be greater than 5, you put a bracket to show that it has to stop at 5. I know this completely sounded confusing but I hope it somewhat helped!
Interval Brackets

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