Algebraic Expressions and sequences
Evaluate each expression if r = 5, s = 2, t = 7, and u = 1.
6 + 3u
9
Name the property of multiplication that is shown by the equation 17x · 1 = 17x.
Identity
Identify the terms, like terms, coefficients, and constants in each expression.
4b + 7b + 5
terms: 4b, 7b, 5;
like terms: 4b, 7b
coefficients: 4, 7;
constant: 5
Add (-7x + 1) + (2x - 11).
-5x - 10
Find the GCF of 6ab, 3a.
3a
Evaluate each expression if a = 4.1, b = 5.7, and c = 0.3.
10 – (a + b)
0.2
Use the Distributive Property to write 6(w + 5) as an equivalent expression.
6w+30
Identify the terms, like terms, coefficients, and constants in each expression.
-5x + 4 - x -1
terms: -5x, 4, -x, -1; like terms: -5x, -x; 4, -1; coefficients: -5, -1; constants: 4, -1
Subtract (11x - 9) - (-4x - 6).
15x - 3
Find the GCF of each pair of monomials.
25f, 60g
5
The expressions c – e, where c stands for the money collected and e stands for the expenses, is used to find the profit from a basketball concession. If $500 was collected and expenses were $150, find the profit for the concession.
$350
Name the property shown by each statement.
(ab) c = c (ab)
Commutative Property
Sari and her friends played miniature golf. There were p people in the group. Each person paid $5 for a round of golf and together they spent $9 on snacks. Write an expression in simplest form that represents the total amount that Sari and her friends spent
$5p + $9
Add (-2x + 4) + (4x + 6).
2x + 10
Factor each expression. If the expression cannot be factored, write cannot be factored.
5x + 35
5(x + 7)
The summer Olympics occur every four years. If the last summer Olympics happened in 2008, when are the next three times that it will occur? Describe the sequence the Olympic years form.
2012, 2016, 2020; This is an arthimetic sequence where the common difference is 4.
Evaluate the expression 3(9 - 16).
-21
Simplify the expression -3(4x + 5) - 2(-5x + 8)
-2x - 31
Two Florida panthers were weighed. One weighs 6x + 21 pounds and the two together weigh 14x + 11 pounds. How much does the other panther weigh alone?
8x - 10 pounds
The area of a rectangular pool is (15x - 9) square units. Factor 15x - 9 to find possible dimensions of the pool.
3 units by (5x - 3) units
The enrollment at Grove Middle School is expected to increase by 40 students each year for the next 5 years. If their current enrollment is 600 students, find their enrollment after each of the next 5 years
640, 680, 720, 760, 800
Name the property that is shown by the equation 5(4 + g) = 5(4) + 5( g).
Distributive
Write the expression 7b - 3(b - 1) in simplest form.
4b + 3
An airline charges $(22x + 20) for a ticket, $(x + 1) to check a bag, $2x for food, and $(15x - 16) to upgrade to first class. Write an expression to represent the total cost of flying first class, checking a bag, and buying food on the plane.
$(40x + 5)
Two friends bought a $14 pizza. Each person bought their own drink. The total cost of the food can be represented by the expression $2x + $14. What expression represents the cost of food for one person?
(x + 7) dollars