# Algebra problems

Complete and please show all the work.

Please see attached file for full problem description.

1. List all the factors of 45.

2. Which number is prime?

A) 1

B) 12

C) 31

D) 99

3. List all the prime numbers between 25 and 60.

4. Find the GCF for 68, 85, and 153.

5. Find the LCM for 18 and 27.

6. Multiply and write the result in simplest form.

A)

B)

C)

D)

7. Add.

8. Subtract. -

9. Evaluate. (3 ? 2 + 1)2

10. Evaluate. (15 - 5) ÷ [(12 ÷ 2 ? 2) - 2]

A) 10

B) 1

C)

D) 8

11. Evaluate. | -48 |

12. Write the following phrase using symbols. Use the variable x to represent the number.

A number decreased by by 6

13. Subtract. -11 - 20

A) 31

B) -9

C) 9

D) -31

14. Divide.

A) -6

B) 0

C) undefined

D) 1

15. Combine like terms.

2r + 10s + 4r

A) 6r + 10s

B) 16rs

C) 12r + 4s

D) 16r + s

16. Divide.

A) m2n3

B) m4n4

C) m2n4

D) m4n3

17. Multiply.

a7 a5

18. Solve. x - 9 = -6

19. Solve. 10x - = 9x +

A)

B)

C)

D)

20. Solve. 8x - 11 = 2x + 1

21. Translate the following statement into an algebraic equaion. Let x represent the number.

3 more than 9 times a number is 4 times that same number.

22. Solve. 8 - (4x - 3) = 19

23. Tickets for a play at the community theater cost $14 for an adult and $2 for a child. If 270 tickets were sold and the total receipts were $2340, how many of each type of ticket were sold?

24. Graph the solution set of x  -1.

A)

-1 0

B)

-1 0

C)

-1 0

D)

-1 0

25. Solve and graph the solution set. 3x  7x + 20

A)

-5 0

B)

-5 0

C)

0 5

D)

0 5

26. Which of the ordered pairs is a solution for the equation 4x - 3y = 12?

A) (0, 4)

B) (-3, 0)

C) (-3, -4)

D) (0, -4)

27. Plot the point with coordinates (-4, 3).

A)

B)

C)

D)

28.

Graph 3x + y = 3.

29. Graph y = 4.

30. Find the slope of the line passing through the points (0, 2) and (-10, 9).

A)

B)

C)

D)

31. Find the slope of the line passing through the points (-2, 2) and (-2, -3).

A) 0

B) 1

C) -5

D) Undefined

32. Find the slope of the graphed line.

A) 2

B) -2

C)

D) -

33. The following pie chart represents the eye color of students in a certain class.

What percentage of students in the class had blue or brown eyes?

34. The line graph below shows the number of trees in a certain seaside town.

(a) Which year had the fewest trees?

(b) Between which two years did the greatest increase in the number of trees occur?

35. Find the slope and y-intercept.

-9x - 8y = -64

36. Find the slope.

7x + 2y = -11

37. Match the graph with one of the equations.

A)

B)

C) y = -3x + 1

D) y = 3x + 1

38. A roof rises 2.75 ft over a horizontal distance of 10.69 ft. What is the slope of the roof to the nearest hundredth?

A) 3.89

B) 0.26

C) 1.60

D) 2.77

39. Determine which two equations represent parallel lines.

(a) y = 5x - 10 (b) y = -5x + 10 (c) y = 5x + 5 (d) y = x - 10

40. Graph the inequality.

y  3x

41. Rewrite the equation 2x - 3y = -6 as a function of x

A)

B)

C)

D)

42. Solve the system by graphing.

x - 2y = 8

x + y = -1

43. Solve the system by addition.

x + y = 1

x - y = 9

44. Solve the system by addition.

-4x + 5y = 5

x - 2y = -2

45. The sum of two numbers is 43. The second is 1 more than 2 times the first. What are the two numbers?

46. Solve the following system of linear inequalities by graphing.

x + 2y  3

2x - 3y  6

A)

B)

C)

D)

#### Solution Preview

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1. List all the factors of 45. = 1, 3,5, 9, 15, 45

2. Which number is prime?

A) 1

B) 12

C) 31

D) 99

3. List all the prime numbers between 25 and 60. 29, 31, 37, 41, 43, 47, 53, 59

4. Find the GCF for 68, 85, and 153. = 17

5. Find the LCM for 18 and 27. = 54

6. Multiply and write the result in simplest form.

A)

B)

C)

D)

7. Add. = 20/21

8. Subtract. - = 10/3 - 5/3 = 5/3

9. Evaluate. (3 · 2 + 1)2=(6+1)^2 = 7^2 = 49

10. Evaluate. (15 - 5) ÷ [(12 ÷ 2 · 2) - 2] = 10/ [(12/4)-2] = 10/ [3-2] =10

A) 10

B) 1

C)

D) 8

11. Evaluate. | -48 | = 48

12. Write the following phrase using symbols. Use the variable x to represent the number. A number decreased by by 6 = x - 6

13. Subtract. -11 - 20

A) 31

B) -9

C) 9

D) -31

14. Divide.

A) -6

B) 0

C) undefined

D) 1

15. Combine like terms. 2r + 10s + 4r

A) 6r + ...

#### Solution Summary

Forty six questions related to finding factors, prime numbers, Greatest common factor, Least common factor, fractions, mathematical operations, solving linear equations, coordinate geometry, graphing, slope intercept form of graphs, inequality graphs, solving a system of equations and word problems.