Equivalent Expressions
Simplify: 7x2 + 12x - 18x2
ANSWER: -11x2 + 12x
7x2-18x2+12x commutative property
-11x2 + 12x combine like terms
Simplify: 3(2x + 5)
ANSWER: 6x + 15
Using the distributive property, multiply each term by 3
3(2x) + 3(5)
6x + 15
What is the greatest common factor of 144 and 9?
Answer: 9
9: 1,3,9
144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144
In the expression: 3x + 7, what is the coefficient?
3
The coefficient is the number that is multiplied by the variable.
An average person blinks 50 times every 2.5 minutes. How many times does the average person blink per hour?
Answer: 1200
50/2.5 = 20 blinks per min
20 x 60 = 1200 blinks per hour
Fill in the blank:
-10x + 4 +5x = 4 + _
Answer -5x
-10x + 4 +5x
-10x + 5x + 4
-5x + 4
Simplify:
1/2 (14x^2 - 12x + 8)
ANSWER: 7x2 - 6x + 4
use the distributive property
multiply each term by 1/2
1/2(14x^2) - 1/2(12x)+1/2(8)
7x^2 -6x+4
Factor using the GCF:
12x + 5
Answer: cannot be factored, the gcf is 1
What is the area of a rectangle with a length of 2 and width of (4x-1)?
Answer: 8x - 2
area = length x width
area = 2(4x -1)
area = 2(4x) - 2(1)
area = (8x - 2) units2
What number is 75% of 150?
Answer: 112.5
of means multiply
0.75 x 150 = 112.5
Simplify:
3/4n + 3m - 1/3n + 1/4n
Answer:
5/12n + 3 1/4m
3/4n + 3m - 1/3n + 1/4n
5/12n + 3 1/4 m
3/4n + 3m - 1/3n + 1/4m
3/4n -1/3n +3m + 1/4m
5/12n + 3 1/4m
Simplify:
-5x+9(4x+12)
ANSWER: 31x + 108
Use the distributive property, then combine like terms
-5x + 9(4x) + 9(12)
-5x + 36x + 108
31x + 108
What is the factored form of 36x + 45y?
ANSWER: 9(4x + 5y)
>> determine the greatest common factor : 9
>> divide each term by GCF: 36x/9 and 45/9
>> write in factored form with the gcf on the outside of the parentheses. 9(4x+5y)
Which expression must be added to 3x − 7 to equal 0?
Answer: -3x +7
-3x + 7 is the additive inverse of 3x -7
additive inverse sum is 0
A group of friends has a dinner bill of $120.They want to leave a 20% tip for the server and pay an 8% sales tax. What is the total cost of their meal?
Answer: $153.60
$120(0.20) = $24 tip
$120(0.08) = $9.60 tax
Total: $120 + 24 + 9.60 = $153.60
What is the perimeter of a triangle with sides of (3x+4), (9x-5) and (7x+5)?
ANSWER: (19x + 4) units
perimeter is the sum of all sides of a shape
P = (3x+4) + (9x-5) + (7x+5)
P = 3x+9x+7x+4-5+5 commutative property
P = (19x + 4) units combine like terms
Simplify:
5.1(2x+4) + 7.3
Answer: 10.2x + 27.7
5.1(2x+4) + 7.3
10.2x + 20.4 + 7.3
10.2x + 27.7
What's the greatest common factor of:
10ab - 25a
Answer: 5a
10ab: 1,2,5,10,a,b
25a: 1,5,25,a
Bryan’s hockey team is purchasing jerseys. The company charges $250 for a onetime set-up fee and $23 for each printed jersey. Write an expression that can represent the total cost of x number of jerseys for the team?
Answer: $250 + 23x
Evaluate :
4/5a - 25/b - c
when a = 15, b = -1 and c = 12
Answer:
Answer:25
4/5a - 25/b - c
4/5(15) -25/-1 - 12
12 + 25 -12
25
Simpify: (3/4 x +7) - (x-10)
Answer:
(3/4 x +7) - (x-10)
3/4x + 7 - x + 10
3/4x -x + 7 + 10
-1/4x + 17
Simplify:
3(4a-9) - 12(a+7)
Answer: -111
3(4a) -3(9) + -12(a) + -12(7)
12a - 27 -12a - 84
12a -12a -27 -84
-111
Factor:
4b^5 + 4b^3+16b^2
Answer: 4b2 (b3 + b + 4)
4b^5 + 4b^3+ 16b^2
gcf: 4b2
4b5/4b2 + 4b3/4b2 + 16b2/4b2
4b2 (b3 + b + 4)
What property is illustrated by:
3x + 9 = 9 + 3x
Answer: Commutative Property
What is the distance from -45 to 29?
Answer: 74
l -45 - 29 l = l -45 + -29 l = l -74 l = 74