Drill #4Evaluate the following if a = -2 and b = ½. 1. ab – | a – b |

Solve the following absolute value equalities: 2. |2x – 3| = 12

3. |5 – x | + 4 = 2

4. |x – 2| = 2x – 7

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

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| = 5where 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 = b 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/c2. If c > 0 and a > b then ac > bc and a/c > b/cNOTE: The inequality stays the same

For negative numbers:3. If c < 0 and a < b then ac > bc and a/c > b/c4. If c < 0 and a > b then ac < bc and a/c < b/cNOTE: 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 StepEx1: y – 6 < 3Ex2: 5w + 3 > 4w + 9Ex3: 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.• < and > get open circles • < and > 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)