Section 2.6 Solving Linear Inequalities and Absolute Value Inequalities

Inequality Inequality- a statement that two quantities are not equal. Uses the signs :,,, Linear Inequality ex. 3x

Solution to Inequality Equation Finite number of solutions Inequality Infinite Solutions

Adding and Subtracting Inequalities Rules are the same as when solving equations: What you add/subtract to one side of the inequality you must do to the other side to make an equivalent inequality.

Multiplying and Dividing Inequalities Rules are the same as when solving equation EXCEPT when negative numbers are involved. Rule: When solving inequalities, multiplying and/ or dividing by the same negative number reverses (flips) the direction of the inequality the sign.

Graphing Inequalities 0 [, ] – number is included (, ) – number is not included (, ) – always used with,

Interval Notation [, ] – number is included (, ) – number is not included (, ) – always used with,

Compound Inequalities Conjunction (Intersection) “And” -3 < 2x + 5 and 2x + 5 < 7 can also be written -3 < 2x + 5 < 7 Solution: Values they share Disjunction (Union) “Or” 2x 3 Solution: Everything

Absolute Value Equations ex.

Meaning of Absolute Value Equation What does it mean? or

Absolute Value Inequalities

Meaning of Absolute Value Inequalities What do they mean?

Absolute Value Answer is always positive Therefore the following example cannot happen... Solutions: No solution

Absolute Value Answer is always positive Therefore the following example can happen... Solution: