Facts and Properties
There are four symbols that make up inequalities... they are:
Greater Than
Less Than
Greater Than or Equal to
Less Than or Equal to
Solve:
x + 17 > 21
x > 4
5 less than a number is greater than 12
x - 5 > 12
Someone from 1875 had $500 in a savings account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. What is the greatest amount of weeks she can withdraw in order for this to be true?
Set up the inequality and solve on the board.
500 - 25w > 200
GREATER THAN OR EQUAL TO 200
She can withdraw for 12 weeks or less
An inequality shows you what a variable could be but also what it...
COULD NOT BE
Solve:
x - 6 < 5
x < 11
1/3 of a number is less than 6
x/3 < 6
Kevin has $25. MP3 downloads cost $0.75 each. How many songs can he download and still have $13 left to spend?
25 - 0.75d > 13
GREATER THAN OR EQUAL TO
He can download 16 or less MP3s
The addition and subtraction properties of inequalities state that if you add or subtract the same number from both sides of an inequality it will remain:
True
Solve:
x - 4 < -12
x < -8
10 times a number is at least 50
10x > 50
GREATER THAN OR EQUAL TO 50
(Jeopardy Labs wont let me write the greater than or equal to symbol)
Janie has $3. She earns $1.20 for each chore she does and can do fractions of chores. She wants to earn enough money to buy a CD for $13.50. How many chores does she need to complete in order to afford her CD?
1.20c + 3 > 13.50
GREATER THAN OR EQUAL TO
c > 8.75
(You cannot do .75 of a chore)
She must do 9 chores or more
When you divide or multiply an inequality by a negative number you must do what?
FLIP (REVERSE) THE SYMBOL (SIGN)
x + 64 > -33
x > -97
4 times a number is less than -2
4x < -2
Omar is currently not writing the answers to his practice problems on his test. If he loses 5 points for every answer but gets 20 point bonus for writing his name. What is the greatest amount of questions he can get wrong and still pass with a 65? A perfect score is 100.
100 - 5x + 20 > 65
GREATER THAN OR EQUAL TO 65
x < 11
Less than or equal to 11
OMAR CAN GET NO MORE THAN 11 QUESTIONS WRONG!
When graphing the inequality x < 6 what kind of circle would you use for the graph?
Open Circle
g + 1,220 < 3,423
g < 2,203
5 times the opposite of a number is less than -14
-5x < -14
The latest online craze is a new game, Khan on Seven. You get 100 points for playing the game. In addition, you get 50 points for each seven-letter word you make with the ten letters you receive. Sal wants to break the record, and he needs 18,000 or more points to do so. How many 7-letter words, w, can Sal make to break the record?
50w + 100 > 18,000
GREATER THAN OR EQUAL TO
w > 358 (greater than or equal to)
Sal must create 358 or more 7-letter words to break the record!