Definitions of Algebraic Properties
Standard 1: Explanations of Simple Equations
Standard 2: Solving Linear Equations & Inequalities
Standard 3: Solving Non-Linear Equations
Standard 4 & 5: Creating Equations & Literal Equations
100
The change in the order of two numbers while adding and multiplying doesn't affect the sum or product is called?
Commutative Property
100
Explain the step or property that was used to get from Line 1 to Line 2.
Line 1: -7x + 22 = 50
Line 2: -7x = 28
Additive Inverse (Subtracted 22 on both sides)
100
Solve for the variable:
50 + r = 20
R = -30
100
Solve for e:
sqrt (e) = 23
E = 529
100
Solve for w.
wc - h = g
w = g + h / c
150
While adding or multiplying numbers, the way in which numbers are grouped by parentheses, does not affect their sum or product is called?
Associative Property
150
Explain the step that was taken from Line 1 to Line 2.
Line 1: 5x = 37
Line 2: x = 7.4
Multiplicative Inverse (divided 5 on both sides)
150
Solve the inequality for w:
2w - 32 > 54
W > 43
150
Solve for b:
sqrt (v-9) + 6 = 56
V = 2509
150
Solve for x:
-3x + 2c = -3
x = -3 - 2c / -3
200
What is it called when you multiply each term in the parentheses by the number on the outside of the parentheses to eliminate the parentheses?
Distributive Property
200
Explain the step that was taken from Line 1 to Line 2:
Line 1: 6(x + 4) = 60
Line 2: 6x + 24 = 60
Distributive Property
200
Solve for the variable v:
V = 15
200
Solve for w:
w2 + 3 = 52
w = (-7, 7)
200
Write the expression.
There are 12 packets of chips in a big pack. I buy "n" big packs of crisps. How many packets of chips have I bought?
expression: 12n
chips = 12n
250
Is the opposite of the number. Any number plus its inverse equals 0.
Ex. a + (-a) = 0
Ex. -5 + 5 = 0
Additive Inverse
250
Explain the step that was taken from Line 1 to Line 2.
Line 1: 7x + 5x + 8 = 28
Line 2: 12x + 8 = 28
Combined like terms
250
Solve the inequality for v:
-3 is less than or equal to v
-3 le v
250
Solve for X:
abs (-4 +5x) = 16
x = {4, -2.4 (-12/5)}
250
The Rock Zoo nurses 37 species of big cats. Recently, a few species of big cats were sponsored to other zoos around the country. The zoo now nurses only 25 species. How many species of big cats were sponsored to other zoos?
Write an equation to represent the problem to help answer the question.
Equation: 37 - c = 25 or 25 + c =37
300
Is the reciprocal of the number. Any nonzero number multiplied by its reciprocal equals 1.
Ex. a x 1/a = 1
Ex. 1/a x a = 1
Multiplicative Inverse
300
Explain how to solve for the variable in the following problem.
5x + 3(x+4) = 28
Distribute the 3, Combine like terms, additive inverse (subtract the 12 from both sides), multiplicative inverse (divide the 8 on both sides to get x by itself)
300
Solve for the variable k:
4k -2(3 - 4k) = 66
k = 6
300
Solve for h:
h = (6, -6)
300
Solve for a:
a = 8 + 4b / g