Writing Algebraic Expressions
Equivalent Expressions
Simplifying Expressions
Expanding Expressions
Factoring Expressions
Adding and Subtracting Expressions
100
More than, plus, combined, all together, increased, and total indicate which operation?
Addition
100
True or False the following three expressions are equivalent:
6t-300 6(t-50) -300 + 6t
True
100
How many groups of like terms are in the following problems.
-2c + 3c - 5 - 4c +7
Two groups: three variable terms -2c, 3c, and -4c
and two constant terms -5 and 7.
100
Which property do we use to expand expressions?
The distributive property.
100
What is the GCF of (12, 84)
12
100
Which two properties do we use to reorder expressions and regroup like terms?
Associative and Commutative
200
You initially open an account with $100, then deposit $20 per month, for m months, into the account. What is the constant term and what is the variable term?
100 is the constant and 20m is the variable term
200
Which property is shown in the following problem?
3(x - 4) = 3x - 12
Distributive Property
200
How do you decide when you can combine (add or subtract) like terms or simplify an expression?
The terms are constants with no variable or they have the same variable and exponent.
200
Does the value of an expression change when expanded?
No the value does not change if expanded it is only an equivalent expression.
200
What is the GCF of (72, 81)
The GCF is 9
200
Add the following expressions
(3x+ 7) + (6x + 8)
9x + 15
300
Evaluate the following expression:
2x + 10, when x is 3.
16
300
Which two properties are shown in the example below?
(5x + 2) + (3x + 4) = (5x +3x) + (2 + 4) = 8x +6
Commutative and Associative Properties of Addition
300
True or False: you can multiply and divide a term with an x and term without like 4x(2) or 4x/2?
True
300
Expand the following expression:
3(n + 7)
3n + 21
300
What is the GCF of 12x + 6
6
300
How does the subtraction sign in between the following two expressions affect the terms in the second set of parenthesis.
Example (4x + 9) - (x - 5)
It flips the signs of the terms inside the parenthesis because it acts like a negative 1 being multiplied by the terms inside the parenthesis.
400
A tank containing 35 gallons of water is leaking at a rate of 1/4 gallon per minute. Write an expression to determine the number of gallons left in the tank after m, minutes.
35 - 1/4m
400
What is an equivalent expression for the following:
3(4x - 10)
12x - 30 or 12x + (-30) or -30 +12x
400
Simplify the expression below
8h + (-7d) - 14 + 5d - 3h
5h - 2d -14
400
Expand the following expression:
-2(3x -4y + 8)
-6x + 8y - 16
400
Facotor the following expression:
14x + 49
7(2x + 7)
400
Add the following expressions
(2x + 3) + (-2x + 9)
12
500
Write an expression to represent the height of a tree that began at 6 feet and increased by 2 feet per year. Let y represent the number of years.
6 + 2y
500
Are the following two expressions equivalent? How can you prove your answer?
-10 + 3x and -3x + 10
No they are not equivalent. You can prove this by substituting the same number in for x in both expressions.
Let x = 1
-10 + 3(1) = -10 +3=-7
-3(1) + 10 = -3 +10 = 7
500
Simplify the expression:
-5v + (-2) + v + v (-2v) + 1
-5v - 1
500
Use the distributive property to expand the following expression then simplify or combine like terms:
7(7x - 3y) - 6 + 2 + 5y
49x - 16y - 4
500
Factor the following expression:
36x + 12y + 24
12(3x + y + 2)
500
Subtract the following expressions:
(-7x - 5) - (6x + 10)
-13x - 15
600
What expression can be used to determine the cost of buying g pounds of granola at 3.25 per pound, and f pounds of flour for $0.74 per pound?
3.25g + 0.74f
600
McClean said that -4n +3 +9n -4 is equal to 4n. What error did he make. What is the correct answer?
McClean combined unlike terms. He subtracted 5n-1 to get 4n.
-4n + 3 + 9n -4 =-4n+9n +3 - 4= 5n - 1
600
Write an expression that can be used to determine the perimeter of a garden if the length is x and the width is 2x -7.
6x - 14
600
Marcellus is expanded the deck on the back of his house. Let x feet represent the increase in length and 8 ft represent the existing length. The width is 5 ft. What is the area?
A=LW A= 5(x + 8) = 5x + 40
600
Mian says that the expression 3 + 5y can not be factored using a GCF is she correct?
No, the GCF of 3 and 5 is 1 and 1 can be counted as a GCF the factored expression however would be the same 1(3 +5y) = 3+5y
600
A= bh/2 b= 10 and h= x + 2
10(x + 2)/2= 5x + 10
A=bh/2 b= 8 and h=x
A=8x/2= 4x
5x + 10 - 4x = x +10 cm2
700
The expression -120 + 13m represents a submarine that began at a depth of 120 feet below sea level and ascended at a rate of 13 feet per minute. What is the submarines depth after 6 minutes?
-120 + 13m = -120 + 13(6)= -120 + 78= -42 feet
700
Explain whether 8t - 3y - 4t is equivalent to 7t + (-3t) - 3y
Yes they are equivalent when you combine like terms 8t - 4t - 3y = 4t - 3y and when you combine like terms for 7t+ (-3t) - 3y = 4t - 3y or the same expression.
700
Simplify the expression:
-(2x + 4) + 3x - 9 + 12 - 10x + x
- 8x -1
700
A gardener plans to extend the length of his rectangular garden. Let x represent the gardens original length. The expression 4(x + 7) represents the area of the extended garden. When asked for the area of the extended portion, the gardener incorrectly states that it was 11 square feet. Describe his error what is the correct answer for the extended portion.
He added 4 + 7 = 11 instead of multiplying 4(x + 7)= 4x + 28 the extended portion is 7 and the entire length is x+7 multiplied by the width of 4 ft.
700
Jordyn is adding to the tile border around her rectangular pool. Let x represent the the width of the pool, in feet. The length is 3 more than 2 times the width, 2x + 3. Write two expressions that give the perimeter of the pool.
P=2w + 2l
P= 2x + 2(2x + 3) = 2x + 4x +6= 6x + 6 or 6(x+1)
700
An art class is making a mural for the school that is shaped like a triangle. The length of the bottom is x. The length of one side is 1 more than three times the length of the bottom. The length of the last side is 2 more than the bottom. What is the perimeter of the triangle.
P = x + x + 2 + 3x + 1 = 5x + 3