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

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• Pre-CalculusLesson 7: Solving InequalitiesLinear inequalities, compound inequalities, absolute value inequalities, interval notation

• Number Line< and > are shown with open circles x4

• Number Line< and > are shown with open circles x4

• Number Line< and > are shown with open circles x4

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

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

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

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

• Example:

• Example:

• Example:

• Example:

• Example:

• Compound Inequalities

• Conjunction Example #1

• Conjunction Example #1

• Conjunction Example #1

• Conjunction Example #1

• Conjunction Example#2

• Conjunction Example#2

• Conjunction Example#2

• Disjunction Example#1

• Disjunction Example#1

• Disjunction Example#2

• Disjunction Example#2

• Disjunction Example#2

• Absolute Value Inequalities

• Less ThanRewrite the inequality as a conjunction.-a < x < aSolve.

• Example

• Example

• Example

• Example

• Greater ThanRewrite the inequality as a disjunction.x < -a or x > aSolve.

• Example

• Example

• Example

• Example

• Interval NotationWhen 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

• 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

• 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

• Write the following statement as an inequality:

x < -3 or 0 < x < 2 or x > 4x < -3 or 0 < x < 2 or x > 4x < -3 or 0 < x < 2 or x > 4http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

• Write the following statement as an inequality:

x < -3 or 0 < x < 2 or x > 4x < -3 or 0 < x < 2 or x > 4x < -3 or 0 < x < 2 or x > 4http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

• Write the following inequality as interval notation: -2 < x < 1 or x > 1

http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

• Write the following inequality as interval notation: -2 < x < 1 or x > 1

http://www.regentsprep.org/regents/math/ALGEBRA/AP1/IntPrac.htm

• Practice QuestionsSolve each inequality, express the answer in interval notation, and graph the solution on the number line.

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