Download Pre-Algebra, Unit 03 Practice Test: Multi-Step Equations

Pre-Algebra, Unit 03 Practice Test: Multi-Step Equations
Name:
Date:
1. Define equality and give an example.
2. Define solution of an equality.
3. Explain why the equation 2 x + 2= 2 ( x + 1) has “all numbers” as a solution.
4. (SE) Which of the following would be the best choice for the first step in solving for x in
the equation below?
2 x + 8 =−10
A.
B.
C.
D.
add 8 to both sides of the equation
subtract 8 from both sides of the equation
multiply both sides of the equation by 2
divide both sides of the equation by −2
5. (SE) What is the value of x that satisfies the equation −3x − 6 =
30 ?
A.
B.
C.
D.
−12
−8
8
12
6. (SE) Five less than twice a number is fifty-three. What is the number?
A.
B.
C.
D.
−29
−24
24
29
HS Pre-Algebra Practice Test
Unit 03: Multi-Step Equations
Revised 2013 - CCSS
Page 1 of 5
7. (SE) What is the solution to the equation below?
−3(2 x − 7) + 4 x =
15
3
−4
−11
−18
A.
B.
C.
D.
8. (SE) What value of x makes the equation below true?
5 x + 4 = 9 x − 12
A.
B.
C.
D.
−4
−2
2
4
9. (SBAC) Three students solved the equation 3(2 x + 3) =
21 in different ways, but each
student arrived at the correct answer. Select all of the solutions that show a correct
method for solving the equation.
A.
3(2 x + 3) =21
6 x + 9 =21
6x 9
21
+ =
6 6
6
9
9
− =
−
6
6
12
x=
6
x= 2
B.
1
1
⋅ 3(2 x + 3) = 21 ⋅
3
3
2 x + 3 =7
−3 =−3
2x 4
=
2 2
x=2
C.
3(2 x + 3) =
21
5 x + 9 =21
+ 9 =+ 9
15 x = 30
15 x 30
=
15 15
x=2
10. Solve −2 x + 3 = 5 x − 18 . Show your work.
HS Pre-Algebra Practice Test
Unit 03: Multi-Step Equations
Revised 2013 - CCSS
Page 2 of 5
11. (SE) A music website sold 68 single songs and 40 albums today. The number of single
downloads has been increasing by 12 each day. The number of album downloads has
been decreasing by 2 each day. If these trends continue, in how many days will the
numbers of single downloads be five times the number of album downloads?
A. 28 days
B. 18 days
C.
6 days
D.
2 days
12. (SE) The cost of renting a car is $65 per day plus $0.25 per mile. Another rental agency
charges $80 per day, but only $0.20 per mile. How many miles would you have to drive
to make the total cost of renting the car the same at both companies?
A.
B.
C.
D.
100 miles
290 miles
300 miles
325 miles
13. (SBAC) For each linear equation in this table, indicate whether the equation has no
solution, one solution, or infinitely many solutions.
Equation
No
Solution
One
Solution
4 x − 1 =−4 x + 1
3 x + 11 = 3 x − 11
4(3 x + 2) = 12 x + 8
2x + 5 =
5
Infinitely
Many
Solutions
14. (SE/SBAC) Choose the best values for P and Q so that the equation will have no
solutions.
2 + 6 ( 2 x − 1=
) 4 ( Px + Q )
A. P = 3 and Q = –1
B. P = 3 and Q = 1
C. P = 2 and Q = –1
D. P = 2 and Q = 1
HS Pre-Algebra Practice Test
Unit 03: Multi-Step Equations
Revised 2013 - CCSS
Page 3 of 5
15. (SE) The table shows the annual fee at two golf courses and the fee each time a member
plays a round of golf.
Course Costs
A. Write and solve an equation to determine the
Course
Annual
Fee for 1
number of rounds of golf for which the total cost
Fee
Round
for 1 year at Course M is equal to Course Q.
M
$600
$20
Show your work.
Q
$450
$25
B. You are able to play an average of 2 rounds of
golf per month. For the year, which course
would be the most economical to play? Explain your thinking.
Long term memory review:
16. Name the quadrant in which the point ( −2,1) lies.
17. Simplify the expression 3(2a + 1) + a.
18. You are given=
a 0.7b − 1.9 ; what is the value of a when the value of b is 14?
A. 11.7
B. 9.8
C. 8.9
D. 7.9
HS Pre-Algebra Practice Test
Unit 03: Multi-Step Equations
Revised 2013 - CCSS
Page 4 of 5
BONUS:
(HSPE) The graph below represents the solution set of an equation.
-8
-6
-4
-2
0
2
4
6
8
Which of these is the equation?
A.
x =2
B.
x =6
C.
x+2 =
4
D.
x+2 =
6
HS Pre-Algebra Practice Test
Unit 03: Multi-Step Equations
Revised 2013 - CCSS
Page 5 of 5