Download Algebra I Name Problem Set 2 Due Date No later than 10/31_ Block

Algebra I
Problem Set 2
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Name _____________________________
Due Date No later than 10/31_ Block _____
Problems are graded for correct answers. There is no partial credit. Each question is worth 1 point.
ALL WORK MUST BE SHOWN or you will receive no credit.
You may work together on problem sets, or you may use your notes and textbook to help you.
Students are not allowed to ask for help on the day the problem set is due.
Problems sets will not be accepted late.
If you are absent the day a problem set is due, you must turn it in the first day you are back in
school.
1.
What is the solution to 3(2 x  1)  3 ?
1
x
A.
3
2
x
B.
3
x 1
C.
x5
D.
1. __________
2.
What is the value of 2x3 y 2 when x   2 and y  3 ?
2. __________
3.
Solve for x:
3. __________
6x 11 13x  7  5x
4.
Which is an example of the commutative property of addition?
A.
7x + 5 = (5 + 2)w + 4
B.
7w + 28 = 7(w + 4)
C.
7w + 4 = 7w + 4
D.
7w + 4 = 4 + 7w
4. __________
5.
What is the solution to 2(4  x)  5 x  8 ?
5. __________
6.
What is the value of the expression 3( x  4)  2 y if x  5 and y   3 ?
A.
-7
B.
11
C.
21
D.
33
7.
If
7. __________
8.
Which statement is ALWAYS true?
4a4a
A.
a  (4  4)  a  0
B.
a44 a
C.
4aa4
D.
8. __________
9.
What property of real numbers guarantees that the second equation
is equivalent to the first?
9. __________
1
t  6  15 , what is the value of t ?
3
A.
21
B.
27
C.
53
D.
63
6. __________
(2 x  1)  5  9
2 x  (1  5)  9
A.
B.
C.
D.
10.
Associative property of addition
Additive inverse property
Commutative property of addition
Distributive property
Translate the following equation and solve for the number:
10. _________
15 less than five times a number x is forty.
11.
What property justifies the following statement?
3x – 11x = (3 – 11)x
A.
B.
C.
D.
Associative Property of Multiplication
Associative Property of Addition
Distributive Property
Reflexive Property
11. _________
12.
What property is illustrated in Step 2?
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
12. _________
7x + 7 + 7x + 11 = (7x + 7) + (7x + 11)
= 7x + (7 + 7x) + 11
= 7x + (7x + 7) + 11
= (7x + 7x) + (7 + 11)
= (7 + 7)x + (7 + 11)
= 14x + 18
A. Associative Property of Addition
B. Commutative Property of Addition
13.
C. Distributive Property
D. Identity Property of Addition
What property is illustrated in Step 2?
Step 1
7 + 8x - 7 - 5x + 3 = 7 + (8x - 7) - 5x + 3
Step 2
= 7 + (-7 + 8x) - 5x + 3
Step 3
= [7 + (-7)] + (8x - 5x) + 3
Step 4
= 0 + (8x - 5x) + 3
Step 5
= (8x - 5x) + 3
Step 6
= (8 - 5)x + 3
Step 7
= 3x + 3
A. Associative Property of Addition
B. Commutative Property of Addition
14.
13. _________
C. Symmetric Property
D. Addition Property of Equality
What property justifies the following statement?
(5x2 + 4) ·
1
(5x2 + 4)
= 1
Answer _________________________________
15.
What is the value of the expression when x 
x 2  3x  2
2
?
3
15. _________
16.
Indicate which property is illustrated in Step 5.
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
8 + 8x - 8 - 6x + 3 = 8 + (8x - 8) - 6x + 3
= 8 + (-8 + 8x) - 6x + 3
= [8 + (-8)] + (8x - 6x) + 3
= 0 + (8x - 6x) + 3
= (8x - 6x) + 3
= (8 - 6)x + 3
= 2x + 3
Answer _________________________________
17.
Which property justifies the work shown:
17. _________
13x – 1 = (12x + 15) + 7x
13x – 1 = 7x + (12x + 15)
A. Commutative Property of Addition
B. Associative Property of Addition
18.
C. Identity Property of Addition
D. Distributive Property
Jim solved an equation and for his final step he wrote 5 = 6.
18. _________
This means:
A. The solution to the equation is 5.
B. The solution to the equation is 6.
C. The equation has no solution.
D. The equation is an indentity and has infinite solutions.
-2x + 6  x – 6
19.
Solve the inequality:
20.
What value of p will make this equation true?
6p  4 4p  8

6
3
A.
B.
C.
D.
-10
-6
2
10
19. _________
20. _________
Algebraic Properties
The algebraic properties listed apply given a, b, and c are real numbers. This is not an exhaustive list of
algebraic properties.