Absolute Value
abs(x+6)=-4
No solution
You can complete about 3 homework problems per minute. Your friend can only do 2 homework problems per minute, but she already had 6 exercises done. How many minutes will it take you to catch up to your friend?
m = # of minutes
m = 6 minutes
3+2(x+4)+x = 5x+5
x=3
u = x - k (solve for x)
x = u + k
When would you only create one pathway?
When the absolute value equation = 0
4abs(x+2)=20
x=3,-7
A new streaming service called "Betflix" offers two yearly pricing plans:
A. $10.00 charge plus $2.50 for each movie rented B. $4.00 charge plus $3.00 per movie.
How many movies will a person need to watch in order for both plans to cost the same amount of money?
m = # of movies
m = 12 movies
8(x+6) + 4=11-4x+5
x=-3
Solve for "a"
12am=4
a = 1/(3m)
What are the names of Ms. Zezzo's two dogs?
Snowy & Dolly
1/3abs(2x+3)-2=6
x=21/2,-27/2
One supplementary angle is 5 more than six times the other angle. What is the measure of each angle?
x = first angle = 25 degrees
6x+5 = second angle = 155 degrees
3(2x-11) = 6x - 33
all real numbers
Solve for "x":
-3x+2c=-3
x=(2c+3)/3
Which situation (in an absolute value equation) would you get "no solution"?
Whenever the absolute value = a negative number.
-3abs(x-7)=-24
x=15, -1
Adam can choose to live in the city or in the suburbs: Option 1: he lives in the city and walks to work for $615. Option 2: he can live in the suburbs for $500 and take the train to work for $5 per day. How many days will he have to work for the options to equal the same amount of money?
d = # of days
d = 23 days
(2+3x)/8=4
x=10
Solve for "a"
u=(ak)/b
a = (ub)/k
What does a true statement mean?
example: 8 = 8
All real numbers or Infinitely many solutions
abs(1/2x+3)=6
x=6,-18
Ms. Zezzo hired a caterer to provide food for her December wedding. The caterer has quoted a price of $90 per person and is asking for a pre-payment of one-fourth of the total bill. If the pre-payment is $1200, how many guests are invited to the party?
p = # of people
p = 40 people
−18 − 6 k = 6( 1 + 3 k)
k = - 1
Solve for "a"
u=a/k
a=uk
When is our test?
Periods 1 & 7: Wednesday (25th)
Period 4: Thursday (26th)