Real Numbers
Solving Linear Equations
Variables on Both Sides
Vocabulary
Mixed Bag
100
The category that describes numbers that can be represented by a fraction
Rational Numbers
100
-3d+10=43
d=-11
100
20x = 5(12+x)
x=4
100
What is the variable in this equation?
3x-7x+45 = 97x+2
x
100
x − 2(x + 10) = 12
x=-32
200
The category containing 0 and the positive integers
Whole Numbers
200
−15 = 5(3q − 10) − 5q
q=3.5
200
14 + 3n = 8n − 3(n − 4)
n=1
200
An equation that is true for all values of the variable has this kind of solution
infinitely many solutions
200
5x-4 = 4x
x=4
300
The difference between natural numbers and integers
Integers contain negative whole numbers and 0
Natural numbers are positive integers without 0
300
What three consecutive integers add up to 204?
67, 68, 69
300
0.5t + 0.25(t + 16) = 4 + 0.75t
Infinitely many solutions
300
A mathematical sentence that states two quantities are equal
An equation
300
p=8
400
Is a rational never, sometimes, or always a whole number?
Sometimes
400
What three consecutive odd integers add up to 75?
23, 25, 27
400
No solution
400
A. 2(x+1) = 4
B. 2x+2 = 4
What property was used to get from line A to line B?
Distributive Property
400
The sum of three consecutive even integers is 30. What are the integers?
8, 10, 12
500
What category of real numbers is:
the product of 3 and pi
Irrational
500
Jenny buys some teas and some coffees. Each coffee costs two times as much as a tea. She bought 4 coffees for $5 each and spent $30.50.
How many teas t did she buy?
Jenny bought 3 teas.
500
A movie club charges a one-time membership fee of $25. This allows members to purchase movies for $7 each. Another club does not charge a membership fee and sells movies for $12 each. How many movies must a member purchase for the total cost of the two clubs to be equal?
5 movies
500
An equation that is true for all values of the variable is called...
an identity
500
A square and a rectangle have the same perimeters. The length of a side of the square is 4x − 1. The length of the rectangle is 2x + 2 and the width is 2x. Write and solve an equation to find x.
x=1