Solving One Variable Equations
Using the equation 570=50𝑥−80, for how many weeks will Hannah need to save before she can pay back her brother and buy the camera?
13 Weeks
Four times a letter n is equal to the opposite of 12.
4n=-12
Solve the following equation:
|x+6.5|=13.4
x=6.9 or x=-19.9
You have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 5.
Write an absolute value equation.
|x-50|=5
Solve for x
4y + x = 10
x=10-4y
Owen borrowed a book with 458 pages from a public library. He read a few pages on day one. On day two, he read twice the number of pages than he read on day one. On the third day, he read six pages less than what he read on the first day.
If Owen read the entire book in these three days, we can model this situation with the equation
x+2x+\(x-6)=458
Solve
110
Nancy deposits $1500 dollars to saving account. She deposits $50 each month. How many months will it take her to reach her total goal of $5000?
Write an equation to model this situation.
1500+50x=5000
Solve Absolute Value Equation
3|x-2| + 14 = 14
x=2
The difference between the temperature on the first day of the month, 𝑡, and the temperature on the last day of the month, 74 degrees, is 6 degrees.
Write an Absolute Value Equation.
|x-74|=6
Solve for W
A=LWXP
W=A/(LXP)
Solve for x:
: 5x+7=3x+4+2x
No solution
A group of friends decides to go out of town to a championship football game. The group pays $185 per ticket plus a one-time convenience fee of $15. They also each pay $27 to ride a tour bus to the game. If the group spent $2,771 in total, how many friends are in the group?
Write an equation to model this equation.
185x+15+27x=2771
Solve:
|2x - 1| + 3 = 6
x=2 or x=-1
A thermometer comes with a guarantee that the stated temperature will differ from the actual temperature by no more than 1.5 degrees Fahrenheit.
Write an absolute value equation that states the temperature is 87 degrees Fahrenheit. Solve
|x-87|=1.5
x=88.5 or x=85.5
Solve for
l: P=2l+2w
l=(P-2w)/2
Georgina wants to mail a package to her sister for her birthday who lives in another state . The cost to mail a package is based on weight. UPS charges $7.50 for the first pound, then $1.50 for each additional pound. FedEx charges $3.50 per pound.
We can use the equation
7.5+1.5(p-1)=3.5p
to model the number of pounds, , a package would have to weight for them to charge the same amount. Solve the equation to find the solution
p=3
City A has a current population of 156,289 residents and has a growth of 146 residents per year. City B has a current population of 151,293 and has a growth of 363 residents per year. To the nearest year, how many years will it take for City A and City B to have the same population?
Create an equation to model this situation.
156289+146x=151293+363x
Solve
−5 |3 + 4 k| = −115
x=5 or x= -13/2
Donna and Kayleigh both go to the same high school. Donna lives 21 miles from the school. Kayleigh lives 6 miles from Donna.
Write an absolute value equation to model this situation.
|x-21|=6
Solve for y
2k+7y=10y
y=(2k)/3
Solve the following Equation:
15 (x + 9) = 24 x + 9 – (9x – 126)
Infinite Solutions
A nutrition store starts a new membership program. Members of the program pay $52 to join and can purchase a canister of protein powder for $42.50 per canister. Non-members pay $49 per canister of protein powder. After how many canisters is the total cost the same for members as it is for non-members?
Write an equation to model this situation.
52+42.50x=49x
Solve:
3 |3 − 5r| − 3 = 18
x= -4/5 or x=2
Jay has money in his wallet, but he doesn’t know the exact amount. When his friend asks him how much he has he says that he has 100 dollars give or take 9.
Write and solve this absolute value problem.
|x-100|=9
x=109 or x=91
Solve for t
5t-2r=25
t=5+(2r)/5 or t=(25+2r)/5