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

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Presentation transcript:

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

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

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

Number Line are shown with open 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

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

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

Example:

Compound Inequalities

Conjunction Example #

Conjunction Example #

Conjunction Example #

Conjunction Example #

Conjunction Example#

Conjunction Example#

Conjunction Example#

Disjunction Example#

Disjunction Example#

Disjunction Example#

Disjunction Example#

Disjunction Example#

Absolute Value Inequalities

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

Example

Example

Example

Example

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

Example

Example

Example

Example

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

Which statement below is the correct interval notation for the situation depicted in this number line graph?

Which statement below is the correct interval notation for the situation depicted in this number line graph?

 Write the following statement as an inequality:  x 4

 Write the following statement as an inequality:  x 4

 Write the following inequality as interval notation:

 Write the following inequality as interval notation:

Practice Questions Solve each inequality, express the answer in interval notation, and graph the solution on the number line