Review your homework with your partner. Be ready to ask questions!!! Friday!!!!

Silent Auction What is a Silent Auction? Bids are not known! Bidders unknown by others!! Eliminates Peer Pressure?

Silent Auction: Question? How many did not check your answers on the website??

Check It Out!! FRIDAY Answers!! All Real Numbers 4. 16/17 or /12 or No Solution 8. -8/3 or /3 or (7.75) x = 250 x = 9 hours x = x = 8.87 hours

Supplies You will need the dry erase markers for our class work!!

Unit 1 Solving Inequalities

Objectives I can write a solution in Inequality Notation and Interval Notation I can solve and graph inequalities with one variable

Number Line

Graphing the Inequalities An open circle indicates the number is excluded from the solution A closed circle indicates the number is included in the solution Draw a number line with at least 3 numbers, plus the direction arrow. Lets do some examples

Open Circles Used when you have the inequality symbols ( ). The open circle means the number being circles is not in the solution. x > 2 Graph: 2 3 1

Closed Circles Closed Circles used when the inequalities are (  or  ). Closed circles mean the number being circles is in the solution set. x  2 Graph: 2 3 1

EXAMPLE 1 Graph simple inequalities a. Graph x < 2. The solutions are all real numbers less than 2. An open dot is used in the graph to indicate 2 is not a solution.

EXAMPLE 1 Graph simple inequalities b. Graph x ≥ – 1. The solutions are all real numbers greater than or equal to – 1. A solid dot is used in the graph to indicate – 1 is a solution.

EXAMPLE 2 Graph compound inequalities a. Graph – 1 < x < 2. The solutions are all real numbers that are greater than – 1 and less than 2.

EXAMPLE 2 Graph compound inequalities b. Graph x ≤ – 2 or x > 1. The solutions are all real numbers that are less than or equal to – 2 or greater than 1.

How many of you have a “nickname” or another name that you are called by? x ≥ 2 Inequality (Set) Notation (INQ) Interval Notation (INT)

These are in Inequality Notation (Set Notation) We are going to change them to INTERVAL NOTATION

What is Interval Notation? [ ] means “included” (equal to) ( ) means “not included” HIGHLIGHT THIS IN YOUR NOTEBOOK! Like a closed dot,, > < Like an open dot,, > <

Infinity??? We ALWAYS use ( ) with infinity!!! All negative numbers All positive numbers HIGHLIGHT THIS IN YOUR NOTEBOOK!

Symbols INQ: Inequality Notation INT: Interval Notation

What would be different for these in Interval Notation?

PRACTICE Graph it on a number line. Change it to interval notation

PRACTICE Graph it on a number line. Change it to interval notation

PRACTICE Graph it on a number line. Change it to interval notation

PRACTICE Graph it on a number line. Change it to interval notation

What would we do if the solution was ALL REAL NUMBERS? Interval Notation?

Practice Complete page 1 of WS 1-2 with your partner.

Solving Inequalities 1.Get the variable terms together on the left side of the equation 2.Move all the numbers to the other side of the equation. 3.DIVISION is the LAST step

Ex 1: 6x + 3 > 5x -2 6x + 3 > 5x –2 x + 3 > -2 (subtracted 5x from both sides) x > -5 (subtracted 3 from both sides)

BIG DIFFERENCE If you multiply or divide each side of an inequality by a negative number then the order of the inequality must be switched.

Ex 2: 3 + 2x < 3x x < 3x – x < 9 (subtracted 3x from both sides) -x < 6 ( subtracted 3 from both sides) x > -6 (divided both sides by –1, switched the inequality sign) x > -6

EXAMPLE 4 Solve an inequality with a variable on both sides Solve 5x + 2 > 7x – 4. Then graph the solution. 5x + 2 > 7x – 4 – 2x + 2 > – 4 – 2x > – 6 x < 3 Write original inequality. Subtract 7x from each side. Subtract 2 from each side. Divide each side by – 2 and reverse the inequality. ANSWER The solutions are all real numbers less than 3. The graph is shown below.

Word Problems You have $500 to replace your bathroom floor tile. The tile cost $370 and the tile saw costs $40 per hour to rent. Write and solve an inequality to find the possible numbers of hours you can rent the saw and stay under your budget.

Solution: Total money: $500 Tile: $370 Saw Rental: $40 per hour Possible Inequality: x ≤ 500 x ≤ 3.25 hours

Homework WS 1-2 Inequalities Keep working on Projects