Properties of Real Numbers
Name the property: 7+4=4+7
Commutative Property of Addition
What property allows you to add the same number to both sides of an equation?
Addition Property of Equality
In the saying "Don't Call Me After Midnight," What does the M in Me stand for?
Move Variables to one side and constants to the other
How many solutions does 3x+5=3x+5 have? And what would the graph look like?
Infinite Many Solutions, One line
Solve for w: P=2l+2w
w = P-2l/2
Name the property: (2+5)+3=2+(5+3)
Associative Property of Addition
What property allows you to multiply both sides of an equation by the same nonzero number?
Multiplication Property of Equality
Solve: 3x−5=16
x = 17
How many solutions does 4x+7=4x-2 have? and what would the graph look like?
No Solution, two parallel lines
Solve for x: y=3x+z
x=y-z/3
Name the property: 6(x+4)=6x+24
Distributive Property
Which property is demonstrated? If x=7, then 7=x.
Symmetric Property of Equality
Solve: 3(x+4)−2=19
x = 3
Determine the number of solutions: 3(2x+4)−x=5x+12
Infinite Many Solutions
Solve for h: A=1/2bh
h = 2A/b
What property is shown by 9+0=9?
Identity Property of Addition
Which property is demonstrated? If x=5 and y=x, then y=5.
Transitive Property of Equality
5x+3=2x+18
x = 5
A student says x=4 is a solution to
3(x+2)=18
Is the student correct?
Yes
Solve for r: C=2πr
r = C/2π
Name the three properties shown in order
8⋅1/8=1
x+(−x)=0
x⋅1=x
Multiplicative Inverse Property
Additive Inverse Property
Multiplicative Identity
Justify each step using the properties of real numbers and equality.
3(x+4)=21
3x+12=21
3x=9
x=3
Given
Distributive Property
Subtraction Property of Equality and Additive Inverse Property
Division Property of Equality
Solve: 4(2x−3)-2x=3(x+3)
x = 7
Determine the number of solutions to the equation. And explain what the solution means.
4(2x−3)+6=8x−6
Infinite many solutions. Any numeric value plugged in for x would make both sides of the equation true
Solve for x. Solve for m. Solve for b.
y=mx+b
x = y-b/m
m = y-b/x
b = y-mx