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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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