Identify the Property
What property is illustrated by the equation 6+(4+x)= 6+(x+4)
What is the commutative property of addition?
9m-27+3m=7m+43
m = 14
Name the smallest set that the number belongs to:
1/16
Rational
How many solutions does this equation have? How do you know without solving?
2x+7=3x
One solution because the variable terms are different
Is the following rational or irrational? Why?
sqrt(169)
Rational - Perfect Square Root
sqrt(169) = 13
Translate the following expression:
4 times the sum of x and 3
4(x+3)
(15+35-2)-:12-5^2
-21
4 (1/4) = 1
The Multiplicative Inverse Property
30+2x=-4(5x-2)
x = -1
Name the smallest set that the number belongs to:
0
Whole Numbers
How many solutions does this equation have? How do you know without solving?
-7-14x-13=-14x-20
Infinite solutions because when you simplify each side of the equation, you have a reflexive statement.
This means that any number can be substituted into the equation, and it will create a true statement.
-14x-20=-14x-20
Is the following Rational or Irrational? Why?
sqrt(19)
Irrational - Imperfect Square Root
This would simplify to a non-repeating, non-terminating decimal.
Translate the following:
6 less than the product of 5 and a
5a-6
9(13*2+9^2)-4
959
If M, A, AND Z represent integers, M + A + Z = Z + A + M is an example of which property?
Commutative Property of Addition
5 + 8(-x - 5) = -2x + 1
x=-6
Name the smallest set that the number belongs to:
sqrt(2/3)
Irrational
How many solutions does this equation have? How do you know without solving?
-(3-6x)=6x+5
This equation has no solutions because the variable terms are the same, but the constants are different.
-3+6x=6x+5
Is the following rational or irrational? Why?
2/sqrt(6)
Irrational because a fraction is a ratio of two integers, and a the square root of 6 is irrational.
Translate the following:
7 more than the difference of d and 3
(d-3)+7
(11-8)-5^2(11+2)
-322
2x+17 = 2x+17
Reflexive Property
(4x + 12) / 4 = 10
x = 7
Name the smallest set that the number belongs to:
-16
Integers
How many solutions does this equation have? How do you know without solving?
-2(x-2)=-3-2x
This has no solutions because the variable terms are same, but the constants are different.
Is this number rational or irrational? Why?
5.7896
Rational because it is a terminating decimal
Translate the following:
12 subtracted from triple d
3d-12
(4+2)^3+(5-14-:7)
219
3x+2=y and y=3x+2
Symmetric Property
10=7(12x+13)-75x
x=-9
Name the smallest set that the number belongs to:
17.234...
Irrational
How many solutions does this equation have? How do you know without solving?
-5(-2-8x)=10+5x
This equation has one solution because the variable terms are different.
Is this number rational or irrational? Why?
sqrt(4/16)
Rational -- This simplifies to a fraction
2/4=1/2
Translate the following:
2 less than double the sum of x and y
2(x+y)-2
6*4-:12+72-:8-9
2