Download ALG 01 - MULTI-STEP EQUATIONS Test Review File

Algebra
Name ____________________________
Instructor ______________ Hr/Blk __
Test 1 Review
Solve each equation.
1.
6=p–8
2.
m
4
7
3.
2j – 13 = 25
4.
n
1 7
5
5.
f 4
5
2
6.
w
7
6 
9
9
7.
4y – 16 + 8y = –4
8.
-2(a + 6) = -22
9.
2x - 7 - (x - 5) = 10
10.
2(3x - 4) = -4(x + 7)
Given the solution sets: Write in both set (-builder) and interval notation and then graph (if needed).
1. a is greater 4.
3.
2. No more than 10 people may use the treadmills at any time.
4.
5.
Solve each inequality. Write in both set (-builder) and interval notation and then graph (if needed).
6.
2x + 7 < 20
7.
-6x + 9 ≥ 21
8.

x
 4  2
5
9.
7 – 3x ≤ 2x + 6
10.
3(2c – 2) – 2c > 0
11.
3x – 5 > 4 or 9 - 2x > 5
12.
-6 < 5m – 1 < 39
13.
6b – 1 ≤ 213 and 2b + 1 ≥ 11
Solve each equation / inequality. Graph the solution set.
It is possible that the equation / inequality has no solution or all real numbers.
1.
| x + 2 | = 11
2.
| x + 16 | = 5
3.
| 3x – 7 | = 5
4.
| 8x + 2 | + 10 = 6
5.
|x–9|>5
6.
| 2x + 3 | < 5
7.
| 7x – 4 | ≥ -38
8.
| 7x – 4 | < -38
9.
12x – 23 = 1 + 4(3x – 6)
10.
8w – 5 > 2(4w – 3)
.
Define a variable and write an equation / inequality for each situation. Then solve.
1. Thirty decreased by the sum of a number and five equals one hundred.
2. A fair charges $7.25 for admission and $5.50 for a ride pass. Ten friends visited the fair. Not all of the friends
purchased ride passes. If their total cost was $105.50, how many friends purchased ride passes?
3. Jasmine is 23 years old. Jasmine is 3 years less than half of George’s age. Find George’s age.
4. Three times a number plus 12 minus 5 times the same number is 22. What is the number?
5. Eli took the fleet of 8 vans for oil changes. All of the vans needed windshield wipers which cost $24 per van.
The total bill was $432. Find the cost of an oil change.
6. Reliable Rentables rents a car for $12.95 per day plus 15¢ per mile. Your company has limited you to $90 a
day for car rental. What is the maximum number of miles that you can drive each day?
MULTIPLE CHOICE
_____ 1.
What value of x satisfies the equation -4x – 9 = -5 – 6x?
A. -7
B. -1
C. 1
D. 2
E. 4
_____ 2.
Solve for x: 2(x – 4) = 17 – 3x
A. -4
9
B.
5
21
C.
5
D. 5
E. 25
_____ 3.
What is the solution of the equation 3 (7x + 8) = -5 (4x + 9)?
69
41
53

41
15

41
1
41
A. 
B.
C.
D.
E. 21
_____ 4.
Which equation has no solution?
A. | m – 4 | – 10 = 159
B. 6n – 1 = 12n + 2
C. 5w + 8 – w = 7w – 2(w – 4)
D. 8 – (2v + 4) = 2v – 4
E. -2x + 3 – 8x = -10x – 3
_____ 5.
Which of the following notations properly reflects the solution set below?
A.
B.
C.
D.
E.
{ x | x < -7 or x > 14 }
{ x | -7 < x < 14 }
{ x | -7 > x > 14 }
( -7, 14 ]
( -∞, -7 ) U [ 14, ∞ )
_____ 6.
What are the solutions of the inequality?
A. x > - 7
x
 2
5
Graph the solutions.
B. x > - 7
C. x < -10
D. x > -10
E. none of the above
_____ 7.
Vis ordered concert tickets which were $3.50 for adults and $2.50 for students.
She ordered 4 more student tickets than adult tickets. Her total bill was $56.
How many of each did she order? What is the equation that represent the problem above?
A. 3.50 (x)
+ 2.50 (4)
= 56.00
B. 3.50
+ 2.50 (x + 4) = 56.00
C. 3.50 (x)
+ 2.50 (x + 4) = 56.00
D. 3.50 (4)
+ 2.50 (x)
= 56.00
E. 3.50 (x + 4) + 2.50 (x)
= 56.00
_____ 8.
Which graphs represents all of the solutions of –z + 7 < 3 ?
A.
B.
C.
D.
E. none of the above
_____ 9.
A carpenter is cutting a 2 by 4 for the framing of a roof. The length needs to be 5 feet. He allows 0.1
foot possible variation for the length of the cut. What values of L represent the acceptable lengths for
the board, in feet?
A. L = 5
B. L > 4.9
C. L < 5.1
D. 4.9 < L < 5.1
E. L < 4.9 or L > 5.1
_____ 10. Which inequality represents the phrase all real numbers that are greater than -7 and less than -4?
A. n > -7
B. n < -4
C. n > -7 or n < -4
D. -7 < n < -4
E. -4 < n < -7
_____ 11. Solve for x: 15 – 2x ≥ 55
A. x ≤ -40
B x ≥ -40
C. ( -∞, -20 ]
D. [ -20 , ∞ )
E. none of the above
_____ 12. What operation should you use to solve -6x = -24?
A. add -6 to both sides
B. add 6 to both sides
C. subtract 6 from both sides
D. multiply by 6 to both sides
E. divide by -6 to both sides
_____ 13. Solve for x: | 2x +10 | = 6
A. 2
B. -2, 2
C. -8, -2
D. -8, 2
E. no solution
_____ 14. What are the solutions of 8 < x + 2 < 12?
A. [ 6, ∞ )
B. [ 6, 10 )
C. [ 6, 14 )
D. [ 10, 14 )
E. [ -∞, 10 )
_____ 15. What is the solution of 2n – 3(4n + 5) = -6(n – 3) – 1?
A. -8
B. -6
C. 
D.
1
4
E. 4
1
2
_____ 16. What are the solutions of | 5a + 5 | > 35?
A. ( -∞, -8 ]
B. [ -8, 6 ]
C. [ 6, ∞ )
D. ( -∞, -8 ] U [ 6, ∞ )
E. ( -∞, ∞)
_____ 17. A merchant is selling wind chimes from a booth at a flea market. He rents his space for $125 per day.
The profit from each wind chime sold is $12. His goal is to make $3500 in a five day work week. Which
equation represents how many chimes he needs to sell in a week to meet his goal?
A. 12c – 625 = 3500
B. 5(12c) + 125 = 3500
C. 5(12c) – 125 = 3500
D. 5(12c + 125) = 3500
E. 5(12c – 125) = 3500
_____ 18. Which compound inequality represents the graph shown to the right?
A. 7d + 1 < 0
B. 7d + 1 > 0
C. 7d + 1 < 1 or 7d + 1 > 15
D. 1 < 7d + 1 < 15
E. 1 < 7d + 1 < 15
_____ 19. ∣4x∣ + 3 < 0
3
A. x < 
4
3

B.  ,  
4

C. both A & B
D. no solution
E. all reals
_____ 20. Which of the following solutions is true for
A.
B.
11
4
1
12
C. 0
D.
E.
3
4
13
4
x 1
 ?
3 4