Simplify and Evaluate
Directions for 1-4: Write the property(ies) used to simplify the expression.
1) 69 + (31 + 23) given
(69 + 31) + 23 ____________
Associative Property of Addition
Solving Equations (use the balance method)
6) 47 = 2d + 5
d= 21
11) 18 less than 5 times n
5n-18
16) A 75-meter rope is cut so that one piece is 13 meters shorter than the other. Define the lengths of the pieces algebraically.
Let x= the shorter rope's length
x+13 = the longer one's length
(there is an alternate answer to this!)
21) At the Berkeley Carroll teacher holiday party, the number of plain pizzas ordered was 5 more than 7 times the number of pepperoni pizzas. If they ordered 101 pizzas, how many plain pizzas were ordered?
89 plain pizzas
2) 11 + (w + 2) given
11 + (2 + w) _____________
Commutative Property of Addition
7) -19x + 7 = 17
x= -90
12) 34 less than n plus 42
(n+42)-34
17) The length of a rectangle is 15 meters less than 4 times the width. Define the dimensions algebraically.
Let x=width
Let 4x-15 = the length
22) Eleven diminished by 5 times a number is the same as 4 times the number increased by 20. Find the number.
x=-1
3) 11+ (2 + w) given
(11 + 2) + w _____________
Associative Property of Addition
8) 4(2x + 5) - 8 = 36
x= 3
13) Eight more than a number equals 12.
8+x=12
18) The sum of 3 numbers is 79. The second number is 9 times the first, and the third is 3 more than the second. Define the three numbers algebraically.
Let x = the first number
Let 9x = the second number
Let 9x+3 = the third number
23) Six times the sum of a number and -1 is the same as 2 more than 8 times the number. Find the number.
x=-4
4) 7(a + b) + 2a - 3b given
7a + 7b + 2a -3b __________________
7a + 2a + 7b -3b ___________________
9a + 4b combining like terms
Distributive Property of Multiplication over Addition
Commutative Property of Addition
9) -3(-4 - 6y) + 7(-y +5) = -8
y =-5
14) A number divided by 41 equals 15.
x/41=15
19) The first side of a triangle is 8 meters longer than twice the second side. The third side is 3 times the second side. The perimeter is 128 meters. Define the lengths of the three sides algebraically.
Let x= the second side's length
Let 2x+8 = the first side's length
Let 3x= the third side's length
24) An ice hockey rink is a rectangle with a perimeter of 174 meters. The length is 9 meters more than twice the width. Find the length and width.
width= 26 m
length = 61 m
5) Simplify the following expression, then evaluate for x = 5
3(2 – x) + 2(3 – x) – (x – 1)
10) -15 - 4x = 6 - 3x
x= -21
15) Nine less than a number equals 72.
x-9 =72
20) Ms. Hartmann is five years less than twice her cousin’s age. The sum of their ages is 46. Define their ages algebraically.
Let x= cousin's age
Let 2x-5=Ms. H's age
25) Ms. Hartmann is five years less than twice her cousin’s age. The sum of their ages is 46. How old is Ms. Hartmann’s cousin?
Cousin is 17.
*This question is 5 years old. How old is Ms. H now???