Basics
Is this correct? If not, at which step did the mistake occur and why?
Step 1: 3(2 - 4)2 - 12
Step 2: (6 - 12)2 - 12
Step 3: ( -6)2 - 12
Step 4: 36 - 12
Step 5: 24
No correct: Step 2 because they distributed the 3 instead of simplifying what is in the parenthesis first
Solve the following proportion:
3 x
4 12
x = 9
Given 6(x - 2) - 5(x - 3) = x + 5 determine whether this equation has no solution, one solution, or infinitely many solutions. Show all of your work and explain why.
6x - 12 - 5x + 15 = x + 5
x + 3 = x +5
No Solution
Solve and graph the following inequality:
-2(x - 4) > 14
-2x + 8 > 14
-2x > 6
x < -3
Create an equation, inequality, or proportion (Do Not Solve)
Andrew is going to open a Jiu Jitsu buisness in either Hammonton or Williamstown. If he opens it in Hammonton he will charge 70 per client and the rent will be $500 per month. If he opens it in Williamstown, he will charge $40 per client and the rent will be $300 per month.
How many clients does he have to have to make the profit the same at both locations?
70x - 500 = 40x - 300
If x = -3, what does the given expression equal?
2x - 3(4 - 5x)
2(-3) - 3(4 - 5(-3))
-6 - 3(4 + 15)
-6 -3(19)
-6 - 57
-63
Chef Rita is cooking for a Sunday brunch. She knows that 44 pancakes can feed 6 people. She is planning on serving 38 people.
Assuming each person eats the same amount of pancakes, set up a proportion to discover how many pancakes Rita must make to feed all 38 people. Your answer must be a whole number.
6 38
44 x
x = 279
Given 2(2x - 1) - 3(3x - 1) = 5x + 1 determine whether this equation has no solution, one solution, or infinitely many solutions. Show all of your work and explain why.
4x - 2 - 9x + 3 = 5x + 1
-5x + 1 = 5x + 1
0 = 10x
x = 0
One Solution
Solve and graph the following:
-2(x + 6) > x + 3 or 2( x + 4) > x + 12
-2(x + 6) > x + 3 or 2( x + 4) > x + 12
-2x - 12 > x + 3 2(x + 4) > x + 12
-12 > 3x + 3 2x + 8 > x + 12
-15 > 3x x > 4
-5 > x
x < -5 or x > 4
Create an equation, inequality, or proportion (Do Not Solve)
Andrew is going to open a Jiu Jitsu business in either Hammonton or Williamstown. If he opens it in Hammonton he will charge 70 per client and the rent will be $500 per month. If he opens it in Williamstown, he will charge $40 per client and the rent will be $300 per month.
How many clients does he have to have such that Hammonton is greater than Williamstown?
70x - 500 > 40x - 300
Simplify the following:
2(x - 3) - 4( x + 1)
2x - 6 - 4x - 4
-2x - 10
Ms. Allen is buying lunch for her students. She knows that 4 hoagies can feed 12 people. She is planning on serving 75 people.
Assuming each person eats the same amount of hoagie, set up a proportion to discover how many she should make for all 75 people. Your answer must be a whole number.
4 x
12 75
x = 25
Given the following formula:
F = 4a + 4b
Solve for b. List all of your steps.
b = F/4 - a
Explain the difference between graphing an "and" inequality and an "or" inequality.
"and" connects
"or" goes opposite direction
Name the smallest set to which sqrt(11) + 3 belongs.
Natural, Whole, Integer, Rational, Irrational, or Real
Explain Why?
Irrational since it can be written as a decimal that does not end nor repeat.
Pick one of the following number sets and explain the type of numbers it includes.
Natural, Whole, Integer, Rational, Irrational, Real
Natural: 1, 2, 3, 4..
Whole: 0, 1, 2, 3, 4...
Integer: ...-3, -2, -1, 0, 1, 2, 3..
Rational: Written as a ratio
Irrational: Can't be written as a ratio
Real: All the above
Is the statement true: 40% of the participants preferred A? Explain your reasoning.
A | B | C | D | Total | |
Boys | 25 | 35 | 10 | 40 | 110 |
Girls | 15 | 10 | 20 | 35 | 80 |
Total | 40 | 45 | 30 | 75 | 190 |
No, 40 people not 40%
ATT charges a $40 sign up fee and $85 per month for an unlimited data plan. T-Mobile charges a $100 sign up fee and $25 per month.
At how many months will the cost be the same?
40 + 85x = 100 + 25x
60x = 60
x = 1
1 month
Jake makes $15 an hour at his job. He pays $2.50 for the bus each way to work. He wants to earn no less than $75 a day.
Write an inequality to represent the situation.
15x - 2(2.50) >= 75
The area of a rectangle is represented by the formula A = lw where l is the length and w is the width.
Shannon is going to be painting her new room. The area of the room is going to be at least 300 square feet. The length of the room is 15 feet. Find the possible widths of the room?
15w >= 300
w>=20
Simplify the following:
-(-(-(-x))) - 4(x - 2)
Solve for when x = -4
-(-(-(-x))) - 4(x - 2) = x - 4x + 8= -3x + 8
20
Is the statement true: The proportion of boys who preferred D is equal to the proportion of girls who preferred D? Explain your reasoning.
A | B | C | D | Total | |
Boys | 25 | 45 | 20 | 30 | 120 |
Girls | 15 | 20 | 15 | 30 | 80 |
Total | 35 | 65 | 35 | 60 | 200 |
No, same amount of people not same proportion
Xfinity charges a $20 sign up fee and $75 per month for an unlimited data plan. Direct TV charges a $90 sign up fee and $45 per month.
Suppose you are signing a contract for a one year plan, which will be cheaper? Explain.
20 + 75x = 90 + 45x
Xfinity= 20 + 75(12) = 920
Direct TV= 90 + 45(12) = 630
Direct TV is cheaper
Lance makes $26 an hour at his job. He pays $7 for the bus each way to work. He wants to earn no less than $200 a day.
Find the minimum amount of hours he must work to reach his goal. Explain your reasoning.
26x - 2(7) >= 200
26x >= 214
x>= 8.12 hours
The area of a rectangle is represented by the formula A = lw where l is the length and w is the width.
Jefferey is painting his room. The area of the room is no more than 260 square feet. The length of the room is 20 feet. Find the possible widths of the room?
Create the equation, proportion or inequality and solve. Be sure to Define your variable.
20w <= 260
w<= 13