2.1/2.2 Solving Inequalities

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Presentation transcript:

2.1/2.2 Solving Inequalities Learning Goals: create equations and inequalities in one variable and use them to solve problems

Interval Notation Symbols Notation used to describe a range of values Many times used in place of set-notation Inequality Symbol Graphing Symbol Interval Notation Symbols include a value ≤ or ≥ ● [ , ] reference a value < or > ○ ( , )

Notations and Their Graphs Set-Notation Interval Notation Graph { y | y > -5 } { y | y ≤ 2 } { y | -2 ≤ y ≤ 7 } { y | y < 4 or y > 6}

Features of Inequalities Inequalities have more than 1 solution When you MULTIPLY or DIVIDE by a negative number you MUST flip the sign. What happens if we multiply the inequality by –1 ?

EX 1 Solve & graph.

EX 2 Solve & graph.

For which values does this hold? compound inequality: a pair of inequalities joined by AND or OR Compound “Key Word” For which values does this hold? What do I shade? Example Graph AND where both are true shade common parts only OR where at least ONE is true shade each part all on the same line

EX 3 Solve & graph.

EX 4 Solve & graph.

EX 5

****Special Cases**** EX 6 Solve & graph.

****Special Cases**** EX 7 Solve & graph.

EX 8 Solve & graph. EX 9 Solve & graph.