Multi-Step Equations
6a + 5a = −11
a = -1
What is the Domain/Input
X
2 < X < 5
(2,5)
f(x) = 2x2 + 3x - 5
39
3(2x + 4) = 30
X = 3
−10p + 9p = 12
p = -12
What is the Range/Output?
Y
2 < X + 3 < 8
(-1,5)
f(X) = 3x2 - 5x + 2
30
5(3y - 2) + 4 = 29
y = 7/3
−11 − 5a = 6(5a + 4)
a = -1
A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer drives 150 miles, how much will they pay in total?
The answer: The total cost for driving 150 miles is 80$
2x - 5 < 3 and 4x + 1 > 9
(2, 4)
f(X) = 2x2 + 3x - 5
39
4(z + 5) -2(z - 3) = 10
z = -8
8 = 8v − 4(v + 8)
v = 10
A local bakery sells two types of cakes: chocolate and vanilla. The chocolate cakes cost $15 each, and the vanilla cakes cost $10 each. If a costumer buys a total of 8 cakes and spends $110, how many of each type of cake did the costumer buy?
y = 8 - 6 = 2
The costumer bought 6 chocolate cakes and 2 vanilla cakes.
2x -3 < 7 and 4x +1 > 9
(2,5)
f(X) = 3x2 - 5x + 2
30
2(3x + 4) = 28
x = 10/3
5(2x + 6) = −4(−5 − 2x) + 3x
X = 10
Black Mesa and Aperture Science are competing to develop advanced technology. Black Mesa has a research team that can produce 5 advanced energy modules per day, while Aperture Science can produce 8 advanced energy modules per day. If Black Mesa starts with 20 energy modules and continues to produce at its daily rate for 7 days, and Aperture Science starts with 15 energy modules and produces at its daily rate for 5 days, how many energy modules will each company have at the end of their respective production periods?
At the end of their respective production periods, both Black Mesa and Aperture Science will have 55 energy modules each.
2x - 5 < 3 and 4x + 1 > 9
(2,4)
f(X) = 3x2 + 2x - 5
51
2(3x + 4) - 5 = 19
x = 8/3