One-Step Equations
2 = z + 7
z= -5
6x + 5 = 29
x = 4
Define a variable. Then write an equation to model each situation.
The total was $28 after a $4 tip was added to the bill.
b = bill
28= 4 + b
3n + 1 = 7
Write an equation to model each situation.
Ten increased by a number is -8
10 + n = -8
-16= t - 6
t = -10
3 - 5y = -37
y = 8
Define a variable. Then write an equation to model each situation.
Nikki's cat is 5 pounds heavier than her sister's cat. If Nikki's cat weighs 9 pounds, how much does her sister's cat weigh?
9 = s + 5
The quotient of a number and 5, less 10, is 3.
n/5 - 10 = 3
Solve the equation
t - 22 = -31
t = -9
-8 = d - 11
d = 3
(2/3)x - 5 = 7
x = 18
Write a real-world situation to represent the equation
s - 45 = -127
Answers may vary. Mrs. Kastens will be the judge.
Amy has saved $725 for a new guitar and lessons. Her guitar costs $475, and guitar lessons are $25 per hour. Determine how many hours of lessons she can afford.
475 + 25x = 725
Solve the equation.
-2k + 7 = -3
k = 5
Which One Doesn't Belong? Explain your reasoning.
y + 4 = 2
x+ 6 = 4
t + 5 = -3
1 + m = -1
t + 5 = -3; the solution to the other equations is -2, but this solution is =8.
(n + 3 ) / 8 = -4
n = -35
Before planting a tree, Sanya digs a hole with a depth 18 inches below ground level. Once planted, the top of the tree is 54 inches above ground. Write and solve an equation to to find the height of the tree that Sanjay planted. (extra 100 points for answer in feet)
(-18) + h = 54
72 inches, or 6 feet
Write about a real-world situation that can be solved using a two-step equation. It should include both multiplication and subtraction.
Answers may vary. Mrs. Kastens will be the judge.
A cell phone company charges $45 a month for service and $0.12 extra for each text message. Ms. Barnes was charged $49.32 last month. Write and solve an equation to find the number of text messages she sent.
45 + 0.12t = 49.32
t = 36 text messages
Solve |x| + 5 = 7
1 = 4 (1/2) - 1 (1/3)p
(Answer must be as a fraction)
p = 2 (5/8)
On one day in Fairfield, Montana, the temperature dropped 85 degrees from noon to midnight. If the temperature at midnight was -21 degrees, write and solve an equation to determine the noon temperature that day.
t + (-84) = -21
63 degrees
Hunter and Amado are each trying to save $600 for a summer trip. Hunter started with $150 and earns $7.50 per hour working at a grocery store. Amado has nothing saved, but he earns $12 per hour painting houses. Write and solve two equations. Who will take longer to save enough money for the trip?
Hunter: 7.50h + 150 = 600; 60 hours
Amado:12h = 600; 50 hours
Hunter will take longer
Marcus has some number of baseball cards, "m". James has some number of baseball cards, "2m + 6". If Marcus and James have 120 cards altogether, write and solve an equation that could be used to find the number of cards in James' collection.
Equation: m + 2m + 6 = 120 or 3m + 6 = 120
m = 38 cards
James' collection = 82