Definitions
The Distributive Property
Equations with Variables on Both Sides
Multi-Step Equations
Equations
100
A term without a variable is called:
A constant.
100
4(x + 7)
4x + 28
100
Solve 8 + 4d = 5d
d = 8
100
Solve 5(15 + d) = 90
d = 3
100
3x = 24
x = 8
200
These types of terms contain the same variables raised to the same powers. Constants are also called this type of term.
Like terms.
200
(y + 6)3
3y + 18
200
11x = 24 + 8x
x = 8
200
Solve 5(a -7) = 24
a = 11.8
200
5(x - 4) = 60
x = 16
300
When a plus or minus sign separate an algebraic expression into parts, each part is called:
A term.
300
-2(x + 9)
-2x - 18
300
5p + 2 = 4p -1
p = -3
300
Solve 2(g + 8) = 4(g - 3)
g = 14
300
8(4q -5) -7q = 20q - 10
q = 6
400
A numerical factor of a term that contains a variable is called the _______________ of that variable.
coefficient
400
-6(g - 2)
-6g + 12
400
21.6 - d = 5d
d = 3.6
400
Solve -6(n + 9) = 4(5n - 7)
n = -1
400
10p - 2(3p -6) = 4(5p -6) -10p
p = 6
500
You have some money. Your friend has $50 less than you. Write an expression in simplest form that represents the total amount of money you and your friend have.
2x - 50
500
Amelia bought roast beef from the deli for $6.85 per pound. Find the total cost if Amelia bought 4 pounds of roast beef.
$27.40
500
Define a variable, write an equation, and solve: Eighteen less than three times a number is twice the number.
Let n = the number. Equation: 3n - 18 = 2n Solution: n = 18
500
Define a variable, give the equation, and the solution: The length of Philip's stride when walking is 4 inches greater than the length of Anne's stride. If it takes Philip 5 steps and Anne 6 steps to walk the same distance, what is the length of Anne's stride?
Let x = the length of Anne's stride Equation: 6x = 5(x + 4) Solution: x = 20 inches
500
Suppose you can rent a car for either $35 a day plus $0.40 a mile or for $20 a day plus $0.55 per mile. Write and solve an equation to find the number of miles that result in the SAME cost for one day.
Let x = number of miles in one day Equation: 35 + 0.40x = 20 + 0.55x Solution: x = 100 miles
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