systems of equations
Elimination: 4x + 8y = 20
-4x + 2y = -30
Answer: X = 7 and Y =-1
(7,-1)
solve: -54 < -5x + 1 < 46
Answer: -9 < x< 11
Madelyn is working two summer jobs, making $8 per hour washing cars and $10 per hour clearing tables. Madeyln must earn no less than $150 per week. Write an inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours clearing tables, c, that Madelyn can work in a given week.
Correct equation: 8w + 10c ≥ 150
Factor : x2 + 6x + 9
answer: (x + 3)(x + 3)
Elimination: 8x + y = -16
-3x + y = -5
Answer: x = -1 and Y= -8
( -1, -8)
Solve: -10 > -x -5 > -16
answer: 5 < x < 11
alexander has p pennies and n nickles. He has a maximum of $0 worth of coins altogther. Write situation as an inequality
Correct equation : 0.01p + 0.05n ≤ 0
factor : x2 - 10x +16
Answer: (x - 2)(x -8)
Elimination: 5x - 3y = -28
4x + 6y = -14
Answer: x= -5 and Y= 1
(-5,1)
Solve : -60 < 5x -10 and 5x - 10 ≤ 25
Answer: -10 < x ≤ 7
A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 28,000 kilograms. Other shipments weighing 9100 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine x, the number of 40- kilograms crates that can be loaded into the shipping container.
Correct equation: 40x + 9100 ≤ 28,000
Answer: x = 472.5
Factor : x2 + 2x - 15
Answer: (x -3)(x + 5)
Substitution: x = 2y + 4
2x + y = 3
Answer: X = 2 and Y = -1
( 2, -1)
Solve: -2x + 6 > 20 or -2x + 6 ≤ 4
Answer: x<-7 x ≥ 1
Eli has $640 to spend at a bicycle store for some new gear amd biking outfits.
* He buys a new bicycle for $356.89
* he buys 2 bicycle reflectors for $16.70 each and a pair of bike gloves for $27.47
* he plans to spend some or all of the money he has left to buy new biking outfits for $74.08
Write and solve an inequality which can be used to determine o, the number of outfits Eli can purchase while staying within his budget
Correct eqaution: 74.08o + 417.76 ≤ 640
Answer: 0 ≤ 3
Factor: x2 + 5x - 6=0
answer: ( x + 6)(x -1)
Substitution: 2x + 3y = 3
y = 2x + 9
Answer: X = -3 and y = 3
(-3,3)
Solve : 2 < 4x +10 ≤ 14
Answer: -2 < x ≤ 1
The jefferson high school band boosters raised more than $5500 for their music scholarship fund. This money came from sales of their marching band performance DVD, which sold of $15. How many DVDs did they sell? Define a variable and write an inequality to solve the problem. Interpet your solution.
Answer: D> 367
Factor: x2 + 12x + 20
answer: ( x + 2)(x + 10)