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Interval Notation and Inequalities

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Open Interval (a,b)(a, b)

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The set of all real numbers xx such that a<x<ba < x < b.

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Half-Open Interval (a,b](a, b]

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The set of all real numbers xx such that a<xba < x \leq b.

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Closed Interval [a,b][a, b]

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The set of all real numbers xx such that axba \leq x \leq b.

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Less Than or Equal To Inequality xbx \leq b

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The set of all real numbers xx that are less than or equal to bb.

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Infinite Interval (,b](-\infty, b]

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The set of all real numbers xx such that xbx \leq b.

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Greater Than Inequality x>ax > a

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The set of all real numbers xx that are greater than aa.

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Absolute Value Inequality xa<b|x - a| < b

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The set of all real numbers xx such that the absolute value of xax - a is less than bb.

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Less Than Inequality x<bx < b

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The set of all real numbers xx that are less than bb.

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Not Equal To Inequality xcx \neq c

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The set of all real numbers xx that are not equal to cc.

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Infinite Interval [a,)[a, \infty)

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The set of all real numbers xx such that xax \geq a.

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Greater Than or Equal To Inequality xax \geq a

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The set of all real numbers xx that are greater than or equal to aa.

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Half-Open Interval [a,b)[a, b)

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The set of all real numbers xx such that ax<ba \leq x < b.

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