Vocabulary
What is a letter or a symbol called that represents an unknown value?
Variable
Solve
9f+4-7f=8
f=2
Solve
abs(x+8)=5
x= -13 and x=-3
Determine if the following equation has one solution, no solution or infinitely many solutions.
6r+3=r-12
One solution
A bill to landscape your yard is $720. The materials cost $375 and the labor is $34.50 per hour. Write and solve an equation to find the number of hours of labor spend landscaping your yard
c=34.50h+720
h=10 hours
In the expression below, what does the 5 represent?
5x+3
coefficient
Solve
6(q-7)-3(4-q)=0
q=6
Solve
abs(4x-3)-14= -1
x= -2.5 and x=4
Determine if the following equation has one solution, no solution or infinitely many solutions.
4(2x-3)=8x-12
Infinitely Many solutions
Planet Fitness charges a $50 membership fee and $20 per month. Crunch charges a $10 membership fee and $30 per month. After how many months is the total cost the same at both gyms?
4 months
In the expression below, what does the 3 represent?
5x+3
Solve
3(x+1)-5=5x+2
x=-2
Solve
3abs(4-3m)=30
m= -2 and m=14/3
Determine if the following equation has one solution, no solution or infinitely many solutions.
6x-5=2(3x+4)
No Solution
Starting from 300 feet away, a car drives towards you at the speed of 48 feet per second. The distance of the car from you after t seconds is given by the equation below. At what times is the car 60 feet from you?
d=abs(300-48t)
t= 5 and t=7.5
How many terms are in the expression below
2x+7-9x+2
4 terms
Solve
19=15w-4(3w-1)
w=5
Solve
abs(x-2)=4x+8
x=-6/5
Provide a value of c for which this equation has no solution.
abs(x+8)=c
Any negative value of c
You conduct a random survey of your small town about having a townwide garage sale. Of those surveyed, 56% are in favor and 44% are opposed. The actual percent could be 5% more or 5% less than the acquired results.
Write and solve an absolute value equation to find the least and greatest percents of your town population that could be opposed to a townwide garage sale.
abs(x-44)=5
x=49% and x=39%