review your homework with your partner. be ready to ask questions!!! friday!!!!
TRANSCRIPT
• Review your homework with your partner.
• Be ready to ask questions!!!
Friday!!!!
Question?
• How many did not check your answers on the website??
Check It Out!!FRIDAY
Answers!!
1. 62. 213. All Real Numbers4. 16/17 or .945. 26. 13/12 or 1.17. No Solution8. -8/3 or -2.79. 4810. -15
11. 29/3 or 9.67
12. 4
13. 25(7.75) + 6.25x = 250 x = 9 hours
14. 425.14 + 45x = 824.14 x = 8.87 hours
Review Parent Function Project
Supplies
•You will need the dry erase markers for our next 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
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 (< or >).
• 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
How many of you have a “nickname” or another name that you are called
by?x ≥ 2
Inequality (Set) Notation (INQ)
Interval Notation (INT) [2, )
These are in Inequality Notation
(Set Notation)
2x 3x83 x
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
INQ 4x
Num Line
INT ( , 4)
INQ 2x
Num Line
INT (2, )
INQ 1x
Num Line
INT ( ,1]
INQ 2 4x
Num Line
INT ( 2,4]
INQ 3 2x
Num Line
INT ( 3,2)
INQ 7 11x or x
Num Line
INT ( ,7) [11, )U
What would be different for these?
[ 3,2]
[ 3,2)
( 3,2)
PRACTICE
Graph it on a number line.
Change it to interval notation
8x
PRACTICE
Graph it on a number line.
Change it to interval notation
5x
PRACTICE
Graph it on a number line.
Change it to interval notation
3 8x
PRACTICE
Graph it on a number line.
Change it to interval notation
3 6x or x
What would we do if the solution was ALL REAL
NUMBERS?
Interval Notation?
),( Inequality
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
ALMOST the same as solving equations!
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.
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 + 9• 3 + 2x < 3x + 9• 3 – 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.
ANSWERThe 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:• 370 + 40x ≤ 500• x ≤ 3.25 hours
Homework
• WS 1-2 Inequalities• Next class you will need the dry erase
markers• Keep working on Projects