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

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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 #1 -3-2 -1 0 1 2

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

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

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

Conjunction Example#2 6 7 8 9 10 11

Conjunction Example#2 6 7 8 9 10 11

Conjunction Example#2 6 7 8 9 10 11

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

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

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

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

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

Absolute Value Inequalities

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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