GRE Algebra and Equation Solving

In this module, you'll learn all of the concepts, techniques and strategies needed to answer algebra and equation-solving questions on the GRE. In particular, this module covers:

Simplifying algebraic expressions
Expanding expressions
3 types of factoring
Basic equations
Equations with fractions
Quadratic equations
Systems of equations
Equations with exponents

Equations with square roots
Equations with absolute values
Strange operator questions
3 types of inequalities
The coordinate plane
Equations of lines
Graphs of quadratics

Two ways to prepare

Beneath most of the video lessons below, you’ll find a Reinforcement Activities box containing practice questions that are specifically related to the concepts covered in that lesson (e.g., the lesson on inequalities). With this lesson format, you have two study options:

Watch the video lesson first and then reinforce your learning by answering several related questions, or…
Tackle the practice questions first and watch the lesson only if you need help with the concepts the practice questions test

For more on this learning strategy, read the “How to Beat the GRE” section of our course overview page.

GRE ALGEBRA AND EQUATION SOLVING VIDEOS

1. Lesson: Introduction to Algebra (5:25)
2. Lesson: Simplifying Expressions (5:44)
3. Question: k's on Both Sides (0:54)
4. Question: Evaluate Expression with 37’s (2:12)
5. Question: Powers of 3 and 5 (1:51)
6. Lesson: Expanding Expressions (7:21)
7. Lesson: FOIL Method for Expanding (3:55)
8. Question: Product with Roots (1:55)
9. Question: Products of Binomials (1:40)
10. Lesson: Factoring – Greatest Common Factor (6:01)
11. Lesson: Factoring - Difference of Squares (4:19)
12. Lesson: Factoring - Quadratics (6:39)
13. Lesson: Combining Factoring Techniques (3:46)
14. Lesson: Simplifying Rational Expressions (6:47)
15. Question: Many Variables vs. 2 (1:41)
16. Question: Simplify Rational Expression (1:30)
17. Question: Tricky Simplification (2:49)
18. Question: 50,002 squared (1:32)
19. Lesson: Basic Equation Solving (5:05)
20. Lesson: Eliminating Fractions (7:38)
21. Question: Equation with Many Fractions (1:06)
22. Lesson: Quadratic Equations (8:37)
23. Question: Rational Sum of Solutions (1:43)
24. Lesson: 2 Equations with 2 Unknowns (9:36)
25. Question: 3x + 2y (1:48)
26. Question: System Question (2:43)
27. Lesson: Number of Solutions to a System (3:37)
28. Lesson: 3 Equations with 3 Unknowns (2:26)
29. Lesson: Equations with Square Roots (8:20)
30. Question: Square Root with x and y (1:02)
31. Lesson: Equations and Powers (4:37)
32. Lesson: Absolute Value Equations (3:46)
33. Lesson: Function Notation (5:01)
34. Question: Functions f and g (1:32)
35. Lesson: Strange Operators (2:22)
36. Question: Integers Between x and y (1:21)
37. Lesson: Working with Formulas (4:26)
38. Lesson: Inequalities - Part I (8:41)
39. Question: (x+2)(x-4) (1:07)
40. Question: 2's, x's and an Inequality (1:38)
41. Lesson: Inequalities - Part II (5:54)
42. Lesson: Inequalities and Absolute Value (6:17)
43. Question: Absolute Inequality Starring p (1:30)
44. Lesson: Quadratic Inequalities (5:21)
45. Question: Quadratic Inequality with x (2:18)
46. Lesson: The Something Method (1:42)
47. Lesson: The Coordinate Plane (3:39)
48. Lesson: Distance Between Two Points (3:30)
49. Lesson: Graphing Lines (8:12)
50. Lesson: Vertical and Horizontal Lines (2:54)
51. Lesson: Slope (5:04)
52. Question: Line M's Slope (1:09)
53. Lesson: x-intercepts and y-intercepts (2:57)
54. Lesson: Slope y-intercept Form (2:59)
55. Question: Variable Slope (1:08)
56. Lesson: Writing Equations of Lines (3:29)
57. Lesson: Graphs of Quadratics (1:23)
58. Question: Which Equation is Best? (1:09)
59. Question: Expansion with Roots (1:41)
60. Question: Functions f and g (1:19)
61. Question: Fraction Within a Fraction (1:52)
62. Question: (x-y)/xy (0:45)
63. Question: x/2 and so on (1:50)
64. Question: 2x vs. y+2 (1:05)
65. Question: Fractions with x and y (1:31)
66. Question: f(4)= (1:06)
67. Question: Sum of Solutions (2:11)
68. Question: Tricky Cubic Equation (1:18)
69. Question: Find the Value (2:14)
70. Question: Sum of Squares (0:56)
71. Question: Some Squared vs All Squared (1:03)
72. Question: Use Intercept to Find Slope (2:04)
73. Question: Distance Between Intercepts (2:58)
74. Question: Power with Binomial Product (2:09)
75. Question: Powers of 2 (1:24)
76. Question: Absolute Solution Sum (1:53)
77. Question: Eighth Powers (2:01)
78. Question: Value of x+2y (1:54)

Total viewing time for the GRE Algebra and Equation Solving module: 248 minutes.

Practice from the Official Guide

Practice the skills and GRE-specific strategies you learned in this module by answering the following questions from the Official Guide to the GRE (3rd edition):

117(5), 118(6), 119(7-8), 120(9), 122(1), 123(3), 156(4), 157(6), 158(9), 161(4), 162(8), 162(10), 163(12), 167(8), 261(2-4), 261(6-7), 262(8), 262(17), 263(18-19)

Here are the related questions in the Official Guide to the GRE (1st or 2nd edition):

112(5), 113(6), 114(7), 115(8-9), 117(1), 118(3), 146(4), 147(6), 148(9), 151(4), 152(7), 153(12), 157(8), 158(10), 243(2-4), 244(5-8), 245(17-20), 246(21)

Note: The above practice questions are listed in the form page#(question#). So, for example, 112(5) represents question #5 on page 112.

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Even More Practice Questions

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