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Pre-Calculus Lesson 7: Solving Inequalities Linear inequalities, compound inequalities, absolute value inequalities, interval notation

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Number Line are shown with open circles x<2x>4

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Number Line are shown with open circles x<2x>4

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Number Line are shown with open circles x<2x>4

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Number Line and are shown with closed circles x 2x 4

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Number Line and are shown with closed circles x 2x 4

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Number Line and are shown with closed circles x 2x 4

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Multiplication Property of Inequality When multiplying or dividing by a negative number, FLIP the INEQUALITY SIGN!

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Example:

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Compound Inequalities

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Conjunction Example #1 -3-2 -1 0 1 2

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Conjunction Example #1 -3-2 -1 0 1 2

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Conjunction Example #1 -3-2 -1 0 1 2

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Conjunction Example #1 -3-2 -1 0 1 2

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Conjunction Example#2 6 7 8 9 10 11

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Conjunction Example#2 6 7 8 9 10 11

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Conjunction Example#2 6 7 8 9 10 11

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Disjunction Example#1 0 1 2 3 4 5 6 7 8 9 10

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Disjunction Example#1 0 1 2 3 4 5 6 7 8 9 10

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Disjunction Example#2 -5 -4 -3 -2 -1 0 1 2 3 4 5

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Disjunction Example#2 -5 -4 -3 -2 -1 0 1 2 3 4 5

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Disjunction Example#2 -5 -4 -3 -2 -1 0 1 2 3 4 5

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Absolute Value Inequalities

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“Less Than” Rewrite the inequality as a conjunction. -a < x < a Solve.

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-4 -3-2 -1 0 1 2 Example

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-4 -3-2 -1 0 1 2 Example

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-4 -3-2 -1 0 1 2 Example

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-4 -3-2 -1 0 1 2 Example

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“Greater Than” Rewrite the inequality as a disjunction. x a Solve.

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Example -5 -4 -3 -2 -1 0 1 2 3 4 5

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Example -5 -4 -3 -2 -1 0 1 2 3 4 5

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Example -5 -4 -3 -2 -1 0 1 2 3 4 5

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Example -5 -4 -3 -2 -1 0 1 2 3 4 5

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Interval Notation When using interval notation: ( means "not included" or "open". [ means "included" or "closed". The inequality would be written as the interval The inequality would be written as the interval

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Which statement below is the correct interval notation for the situation depicted in this number line graph? http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

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Which statement below is the correct interval notation for the situation depicted in this number line graph? http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

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Write the following statement as an inequality: x 4 http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

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Write the following statement as an inequality: x 4 http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

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Write the following inequality as interval notation: -2 1 http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

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Write the following inequality as interval notation: -2 1 http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

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Practice Questions Solve each inequality, express the answer in interval notation, and graph the solution on the number line. 1. 2. 3. 4. 5.

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