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Solving Algebraic Equations and Functions: A Comprehensive Guide

This guide covers a variety of mathematical concepts, focusing on solving algebraic equations, inequalities, and functions. Key topics include calculating shipping costs, solving for slope and dimensions of fields, evaluating expressions, and graphing linear equations. Learn to apply the distributive property, factor equations, and analyze data using measures of central tendency. Each section provides ample examples, from evaluating expressions to graphing inequalities, making it suitable for students seeking to enhance their algebra skills.

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Solving Algebraic Equations and Functions: A Comprehensive Guide

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  1. Final Review

  2. 1. Jon paid 129.95 for 3 DVD’s plus shipping and handling. If the price of each DVD was $40, what was the price of shipping and handling?

  3. What is the solution to the equation: 3(2x – 6) = 4(x + 4)

  4. What is the solution to: 5 – 3x > -13

  5. Use the distributive property to simplify: 3x(x2– 8)

  6. 5. What is the slope of the line passing through the points (-5, 3) and (-4, -7)?

  7. Which of the following is a function rule • for the table shown below? • y = 2.5x + 5 (B) y = 3.75x + 2.5 • (C) y = 4x + 1 (D) y = 5x

  8. Solve the inequality |2x + 6| < 10

  9. 8. Solve the system of equations: 2x + 3y = 13 and y = 2x – 1

  10. 9. Two cars get an oil change at the same service center. Each customer is charged a fee x (in dollars) for an oil change plus y dollars per quart of oil used. The oil change for the care that requires 5 quarts of oil costs $22.45. The oil change for the car that requires 7 quarts of oil costs $25.45. Find the fee and cost per quart of oil.

  11. 10. The perimeter of a rectangular playing field is 260 feet. If tits length is 2 feet less than 3 times the width, what are the dimensions of the field?

  12. 11. Evaluate |-3f + |6g| for f = -3 and g = -5.

  13. 12. Which of the measures of central tendency is most affected if a data item is an outlier?

  14. 13. If you have a 6 sided number cube and a coin, what is the probability of rolling either a 1 or a 2 and flipping heads?

  15. 14. Find the next number in the sequence: 1, 4, 9, 16, 25, 36, 49, …..

  16. 15. Find the product: (2x3y2)(-6x4y3)

  17. Factor: x2– 14x + 45

  18. 17. Simplify:

  19. 18. Simplify:

  20. Solve the equation: x2– 81 = 0 by factoring.

  21. 20. Solve the system of equations: 2x + 5y = 3 and 3x + 10y = -3

  22. 21. What is the domain of the relation (1, 2), (3, 4), (5, 6), (7, 8)?

  23. 22. Solve the system of equations: 3x – 7y = 5 and 9y = 5x + 5

  24. 23. Write the equation of the line of best fit. (See Standards Review Test 3, #29 or #30)

  25. 24. Write the phrase “five times the quantity of two times a number minus 11” as an algebraic expression.

  26. 25. Write the numbers listed in order from least to greatest:

  27. Simplify: 3(2x + 5) – 4(-2 + x)

  28. 27. What is the value of the proportion?

  29. 28. Johnny sells slices of pizza at the county fair. The amount chard for a slice, s, is based on the cost of a plain slice of pizza plus an additional charge for each topping, t, as shown in the equation s = 0.75t + 2. What do the number 2 and the number 0.75 represent in the equation?

  30. 29. What is the solution of the equation?

  31. 30. Is the ordered pair (3, -1) a solution to the equation 5x + 2y = 13?

  32. Is the set of ordered pairs a function? Why or why not? (4, 5), (3, 2), (2, 0), (1, 1), (1, -1)

  33. 32. What is the equation of the line that passes through the points (5, -2) and (4, 0) in slope-intercept form?

  34. 33. What is the equation of the horizontal line that passes through the point (4, -6)?

  35. 34. Solve:

  36. Solve: -3 < 6x – 15 < 27

  37. Simplify: (4x2 + 5x – 11) + (8x2 – 7x – 3)

  38. Simplify: (3x2 – 2x + 5) – (4x2 – 11x + 2)

  39. 38. Make a box and whisker plot for the following data: 76, 80, 96, 98, 100, 98, 91, 89, 82. Identify the median, range, interquartile range, lower quartile, and upper quartile.

  40. Factor the expression: 14x4 – 28x3

  41. Factor the expression: x2- 81

  42. 41. Graph the equations below. A.

  43. 4x – 8y = -12

  44. x = -3

  45. 42. Graph the following inequalities x < 5 x > - 3 x < 2 and x > 5 D. x < -3 or x > 6

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