Drill #4 Evaluate the following if a = -2 and b = ½. 1. ab – | a – b | Solve the following absolute value equalities: 2. |2x – 3| = |5 – x | + 4 = 2 4. |x – 2| = 2x – 7

Drill #9 Solve the following equations: Check your solutions! 1. 2|x – 2| + 3 = |2x + 4| + 2 = –1 3. |2x + 2| = 4x + 10

Writing Absolute Value Equations from Word Problems* Find the value that is + or –. This will be the value that is on the opposite side of the abs. val. Find the middle value. This value will be subtracted from the variable in the abs. val. Example: expected grade = 90 +/- 5 points this translates to |x – 90| = 5 where x = test grade

1-5 Solving Inequalities Objective: To solve and graph the solutions to linear inequalities.

Trichotomy Property Definition: For any two real numbers, a and b, exactly one of the following statements is true: a b A number must be either less than, equal to, or greater than another number.

Addition and Subtraction Properties For Inequalities 1.If a > b, then a + c > b + c and a – c > b – c 2.If a < b, then a + c < b + c and a – c < b – c Note: The inequality sign does not change when you add or subtract a number from a side Example: x + 5 > 7

Multiplication and Division Properties for Inequalities For positive numbers: 1.If c > 0 and a < b then ac < bc and a/c < b/c 2.If c > 0 and a > b then ac > bc and a/c > b/c NOTE: The inequality stays the same For negative numbers: 3.If c bc and a/c > b/c 4.If c b then ac < bc and a/c < b/c NOTE: The inequality changes Example: -2x > 6

Non-Symmetry of Inequalities If x > y then y < x In equalities we can swap the sides of our equations: x = 10, 10 = x With inequalities when we swap sides we have to swap signs as well: x > 10, 10 < x

Solving Inequalities We solve inequalities the same way as equalitions, using S. G. I. R. The inequality doesn’t change unless we multiply or divide by a negative number. Example #1*: Single Step Ex1: y – 6 < 3 Ex2: 5w + 3 > 4w + 9 Ex3: 5x – 3 > 4x + 2

Set Builder Notation Definition: The solution x > 5 written in set- builder notation: {x| x > 5} We say, the set x, such that x is greater than 5.

Graphing inequalities Graph one variable inequalities on a number line. get open circles get closed circles For > and > the graph goes to the right.  (if the variable is on the left-hand side) For < and < the graph goes to the left.  (if the variable is on the left-hand side)

Solve Multi-Step Inequalities: Examples (On board)