Solving Single Variable Equations
Solve for x: 4x – 5 = 3.5x + 7.1
x = 24.2
Solve the formula A = (1/3)bh for h in terms of A and b
h = 3A / b
A company charges $300 for a one-time set-up fee and $28 per item. Write an expression for the total cost of x items.
28x + 300
Translate: "Five increased by four times a number."
5 + 4n
Before: 4(3x + 6) – 9 = 8x + 15
After: 4(3x + 6) = 8x + 24
What property makes this possible?
Addition Property of Equality
Solve the equation 3(4x – 2)/2 = x + 4
x = 2/10
Solve for a in terms of b, c, and g when g = b - ca
a=(g - b)/ -c
Jamie sells x adult tickets at $7.25 each and 15 student tickets at $5.00 each. Write a function f(x) for the total money collected.
f(x) = 7.25x + 75
Translate: "The product of 4, and a number decreased by 7"
4(n - 7)
Before: 3(4x – 8)
After: 12x – 24
What property makes this possible?
Distributive Property
Solve algebraically: (1/5)(5x + 15) = 12
x = 9
The formula for the surface area of a cone is S = πr² + πrl. Solve for l in terms of S, π, and r.
l = (S – πr²) / πr
Mia has $3.10 in dimes and quarters. She has three more dimes than quarters. Which equation can be used to find the number of quarters x?
0.25x + 0.10(x + 3) = 3.10
Translate: "Twelve times, a number increased by 6"
12(n + 6)
Before: 12x + 2x + 4 + 6 = 4x + 20
After: (12x + 2x) + (4 + 6) = 4x + 20
What property makes this possible?
Associative Property
Solve the equation 4(3x + 6) – 9 = 8x + 12
x = -3/4
Solve for b: Rearrange the formula for the area of a trapezoid A = (1/2)(b1 + b2)h to solve for b2.
b2 = (2A / h) – b1
A book store has decided to sell Jason's Graphic Novel. The novel will sell for $15.50 a copy. If it costs Jason $300 to make 24 copies of his novels, how much money will he make if he is able to sell 20 copies of his novels?
$10
Translate: "The quotient of fourteen and triple a number."
14 / (3n)
Before: 8x + 24 + 6x = 20
After: 8x + 6x + 24 = 44
What property makes this possible?
Commutative Property
Explain two ways you could solve 20 = 5(−3 + x)
(1) Divide by 5 first
or
(2) Distribute the 5 first.
Solve for x in terms of a: 5(ax + 4) – 4ax = 40 + 4a
x = (20 + 4a) / a
Billy is remodeling his house and is currently working on painting the exterior of his house. Billy knows that the surface area of the exterior of his house is 1,300 square feet. Billy already has 2 gallons of paint. If one gallon of paint will cover 400 square feet, how many more gallons will Billy need to buy to finish painting his house?
2 gallons
Given 3n - 2, write a verbal expression that matches this mathematical expression.
- three times a number decreased by two
- triple a number minus two
- two less than three times a number
- three times a number diminished by two
- the product of three and a number, reduced by two
Before: 8x = 44
After: x = 44 / 8
What property makes this possible?
Division Property of Equality