# Basic algebra practice

1. Solve. 3(x - 2) - 2x = x - 6

A) Identity B) 0 C) No solution D) 1

2. Find the GCF for 21, 28, and 35.

3. Find the LCM for 6, 28, and 48.

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

x + 2y <= 3

2x - 3y <= 6

5. Evaluate.

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

7. Evaluate. 0 + (-20) + 1 + (-7)

8. The daily low temperatures in degrees Fahrenheit for a certain week were

-3, 1, 4, -5, -10. What is the range of low temperatures for that week?

9. Solve. 19x - 3(5x - 0.065) = 3x + 0.615

10. Marcie gets paid $1.25 an hour to baby sit her little brother. If she baby sits for 3 hours, how much money do Marcie's parents owe her?

11. Evaluate. 8 + 2 ? 5 - 24 ÷ 6 ? 2

12. Evaluate if m = -2, n = 4, and p = -1.

13. Solve. x/6 + 3 = 9

A) 51 B) 36 C) -36 D) -51

14. Graph the solution set of x >=-3.

15. Is -4 a solution to the equation 7x - 5 + 3x = 6 + x - 10

16. Find the mean and the median.

-2, -7/4, 3/4, 4, 9

17. A cylinder has a radius of 5 in. If the volume of the cylinder is 250 in.3, what is the height of the cylinder? [Hint: The volume of a cylinder is given by V = r2h.]

18. How long will it take a bus traveling at 60 mph to overtake a car traveling at 40mph if the car had a 1.5 hour head start?

19. Ricardo is 4 years less than twice as old as his sister. The sum of their ages is 20. How old is Ricardo?

20. Find four consecutive integers such that the sum of the first three is 60 more than the fourth.

21. Solve and graph the solution set. 5x + 4 >= 4x + 9

22. The perimeter of an equilateral triangle is 7 in. more than the perimeter of a square. The side of the triangle is 5 in. longer than the side of the square. Find the length of each side of the triangle. (Note: An equilateral triangle has all sides equal)

23. Solve and graph the solution set. 3x >= 7x + 20

24. Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum and paid $2.00. Find the cost of a chocolate bar and the cost of a pack of gum.

25. An employee who produces x units per hour earns an hourly wage of y = 0.50x + 11 (in dollars). Find the hourly wage for an employee who produces 11 units per hour.

26. Solve. 23x - 6(2x - 0.055) = 10x + 0.515

27. Solve. 4(7x + 10) = 3(9x - 5) + 20

28. Solve: 4x/9 - 6x/7 = 4/63

29. Graph x + y = -2.

30. Graph using the intercept method: 5x - y = 5.

31. Graph by first solving for y.

2x + 3y = 12

32. Find the slope of the line passing through the points (-7, 4) and (8, 4).

33. Find the slope of the graphed line.

34. Which of the ordered pairs is a solution for the equation 5x - 4y = 20?

A) (-4, -5) B) (0, 5) C) (0, -5) D) (-4, 0)

35. Find the slope and y-intercept.

9x - 2y = -10

36. The equation y = 8x - 60 describes the amount of money a class of students might earn from candy bar sales. What are the slope and y-intercept of this line?

37. Find the slope of any line parallel to the line through points (12, 4) and (6, 3).

38. Find the slope of any line perpendicular to the line through points (8, 11) and (10, 9).

39. Write the equation of the line with x-intercept (-4, 0) and y-intercept (0, 6).

40. Write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = -3x + 1.

41. Graph the inequality.

2x + 3y > 6

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

3x + 4y <=12

x + 3y <= 6

x >= 0

y >= 0

43. Rewrite the equation 4x - 10y = 11 as a function of x.

44. Solve the system by graphing.

x - 2y = 8

x + y = -1

45. The sum of two numbers is 35. Their difference is 11. What are the two numbers?

46. Solve the system by substitution.

3x - y = -7

x + y = -9

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

3x - y < 2

x + y > 2

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

x - y <= 3

x + 2y >= 6

49. Lane invested $22,000, part at 8% and part at 7%. If the total interest at the end of the year is $1,710, how much did she invest at 8%?

A) $18,000 B) $16,000 C) $5,000 D) $17,000

50. Given f(x) = 3x + 1, find f(a + 3).

A) a + 10 B) a + 7 C) 3a + 10 D) 3a + 4

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