Simplifying Expressions
Module 3
Simplify each expression.
1.
3x + 7x − 2x
____________________
2.
5(7x)
____________________
3.
−23x + 5y + 7x − 31y
____________________
4.
1
3 1
3
x+ − x+
2
5 4
10
____________________
5.
3(4x) − 7(2x) + 4(5)
____________________
6.
1
1
2
4
(12x) + (10x) − (12x) + (10x)
3
5
3
5
____________________
Write a simplified expression to represent each situation. Show all of your steps.
7. Sophia buys 3 bags of Skittles, and Nina buys 7 bags of Skittles. Assuming that
all bags of Skittles contain the same amount of Skittles, write an expressions to
calculate the total number of Skittles that Sophia and Nina have.
_____________________
identify variable
____________________
expression
8. Mr. Dobalina has 4 classes and each of them had 5 groups of students.
Assuming that all of the group has the same number of students, write an
expression that will calculate the total number of students that Mr. Dobilina has
in his classes.
_____________________
identify variable
____________________
expression
Use the distributive property to write each expression as a sum/difference.
9.
5(x +10)
10.
12(3x + 5)
11.
1
(18x + 28)
2
12.
16x − 24
8
13.
−5(2x − 7)
14.
−21x + 24
−3
Use the distributive property to write each expression as a product.
15.
3x + 9
16.
12x +18
17.
16x − 24
8
18.
100x −100y
18.
1
3
x+
4
4
20.
−21x + 24
−3
Write 2 expressions to represent each situation.
21. Matthew runs a lunch truck. He sells hot dogs for $2 each and Cheeseburgers
for $5. He is open for business 5 days a week. Write two expressions to
represent the total amount of money Matthew takes in over the 5 days.
22.Madison works loading trucks. On each truck she puts 45 boxes of tile and 50
boxes of grout. She loads 35 trucks per day. Write two expressions to
calculate the total number of pounds Madison loads on the trucks each day.
Calculate the pounds if each box of tile weighs 30 pounds and each box of grout
weighs 10 pounds.
Completely simplify each expression. Apply all of the properties that we have been
using, and be especially careful with they – signs.
23.
6(9x + 4) + 3x
24.
5(x − 3) + 2(9x + 2)
25.
8x +16
4x + 8
26.
30x − (6x + 4)
27.
42 − 24x
− 3(9x + 4)
6
28.
9(2x − 3) − 4(2x − 7)
29.
2
4
(9x +12) + (25x − 30)
3
5
30.
16x + 24 10x + 35
•
2x + 7 14x + 21