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*Pre-Calculus Lesson 7: Solving Inequalities Linear inequalities, compound inequalities, absolute...*

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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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