Integers
Negative
In order to solve equations, our goal is to ________ the variable.
Isolate
When solving inequalities, when you multiply or divide by a negative to solve for your variable, you must ______ the symbol.
Flip
When we change a percent to a decimal, we move the decimal ____ spaces to the ______.
2 spaces to the left.
Are the following two expressions equivalent? Explain why or why not.
-7x + 21
-7(x - 3)
Yes. The distributive property.
|-568| =
568
What is the inverse of multiplying?
What is the inverse of addition?
Dividing, subtracting
Give an example of a graph for the following:
1. x ≥ 1
2. x < 10.5
3. x ≤ -9
1. Closed circle, pointing to the right
2. Open circle, pointing to the left
3. Closed circle, pointing to the left
What is 87.5% as a decimal?
0.875
John wrote 1/5 of a paper in 1/4 of an hour. How long did it take him to write the entire paper?
1 hour and 15 minutes or 75 minutes.
1/4 divided by 1/5 = 5/4
5/4 times 60 minutes = 75 minutes
Which expressions would result in the smallest number?
a. -10(-5)
b. -10 + (-5)
c. 10 + (-5)
d. -10 + 5
B = -15
Solve the equation: 5x + 7 = -13
x = -4
Gavin earns $7 for each lawn he mows. He wants to earn at least $45. Write an inequality to show how many lawns Gavin could mow. Solve the inequality and state your answer in a sentence. (Remember, we are talking about LAWNS in this problem)
7x ≥ 45
x ≥ 6.4
He has to mow at least 7 lawns.
What is 8% of $25.30? Think if you were tipping someone at a restaurant! You must round correctly to receive points!
Lucy charges $6 to rake leaves in her neighborhood. Last week, she rakes leaves in 4 yards. She put 2/3 of her earnings in her savings account. How much did Lucy save?
$16
6 times 4 = 24 / 2/3 = 16
Fill in the blank: -10 + ___ = 0
10
Solve the equation: 5(2x - 12.5) = 80
x = 14.25
Ziad needs to collect at least 140 cans for a food drive to earn community service credit. He has already collected 84 items. Write, solve, and graph the inequality for this problem
x + 84 ≥ 140
x ≥ 56
Closed circle, pointing to the right
Addy found that about 40% of 80 classmates at school like hip-hop music. However, 30% of her 60 relatives like hip-hop. How many classmates like hip-hop? How many relatives like hip-hop? Do more classmates or relatives like hiphop? Must answer all three questions for credit!
Classmates: 32
Relatives: 18
More classmates like hiphop than relatives.
Jess is doing a probability experiment with her classmates. She has a bag of marbles with different colors. In the bag there are 5 blue, 8 red, 4 green, 4 yellow, and 9 orange marbles. What is the probability and likelihood she will select an orange marble?
9/30 = .3 = 30%, unlikely
Describe a real world situation to show how adding opposites will result in a sum of zero. Be specific, use integers and write a math sentence representing your situation.
Example: Gaining 5 years, then losing 5 yards. 5 + (-5) = 0
A gym charges a one-time registration fee and a monthly fee. If someone pays a total of $95 after 3 months, and the monthly fee is $25, what is the registration fee?
$20
Solve: -34 < -2(4x - 1)
4.5 > x or x < 4.5
Suhaib's Middle School's basketball team won 75% of their games. If they lost 4 games, how many games did they win?
They won 12 games. They played 16 games total. So 16 - 4 = 12
75% they lost
25% they won
0.25x = 4
x = 16 (total)
16-4 = 12 (win)
JT has a circular swimming pool. The diameter of the pool is 15 feet. What is the area of the swimming pool? Use 3.14 for pi and round your answer to the nearest tenth.
3.14 times 7.5 squared = 176.6 ft squared.