Equations/
Inequalities
Inequalities
A video rental store charges a $20 membership fee and $2.50 for each video rented. Write a linear equation to model this situation. If a new member paid the store $67.50 in the last 3 months, how many videos were rented?
Y=2.50x+20
Y= 67.50 x= 19
19 Videos rented
Identify the solution:
−𝟒𝐲−𝟏𝟏𝐱=𝟑𝟔 𝟐𝟎=−𝟏𝟎𝒙−𝟏𝟎𝒚
(-4,2)
Since March 1920, the population of the city of Pennsauken has grown according to the mathematical model y=720500(1.022) x, where x is the number of years since March 1920. Explain what the numbers 720,500 and 1.022 represent in this model.
Initial Value (population) --> 720500
1.022 --> Growth Rate of 2.2%
Multiply: (𝒙+𝟔𝒚)(𝟔𝒙𝟐−𝒙𝒚−𝟐𝒚𝟐)
6𝑥3+35𝑥2𝑦−8𝑥𝑦2−12𝑦3
Identify x and y intercept:
𝟑𝒚=−𝟏𝟐𝒙+𝟗
X-Intercept = (0.75,)
Y-Intercept = (0,3)
Identify the solution:
𝟐𝒙+𝟖𝒚=𝟔
−𝟓𝒙−𝟐𝟎𝒚=−𝟏𝟓
Infinite Solutions
Your Mac cost $1500 but it depreciates in value by about 18% each year.
a) Write an equation that would indicate the value of the computer at x years.
b) How much will your computer be worth in 6 years?
a) Y=1500(0.82)x
b) Worth 456.01
Factor out the GCF:
𝟐𝟖𝒎𝟒+𝟒𝟎𝒎𝟑+𝟖
4(7𝑚4+10𝑚3+2)
Simplify this inequality:
𝟕−𝟕(𝒙−𝟕)>−𝟒+𝟓𝒙
x<5
John was cleaning out the couch cushions and fund dimes and nickels, 80 coins in all. He counted out the coins and it came to $6.60. How many of each coin did he find?
28 Nickels 52 Dimes
Job A (DOCTOR) has a starting salary of $20,000 with yearly increases of $1500. Job B (TEACHER) has a starting salary of $10,000 with the salary 25% increase each year. What type of function is represented by each plan? Write the equation in for each in function notation.
Job A is Linear f(x)=1500x+20000
Job B is Exponential f(x)=10000(1.25)x
Factor:
𝒙𝟐−𝒙−𝟑𝟎
(𝑥−6)(𝑥+5)