Mastering Algebraic Expressions and Equations for GRE Quantitative Reasoning
Quantitative Reasoning is a cornerstone of the GRE. A strong grasp of algebraic expressions and equations is fundamental to tackling a wide range of problems, from basic arithmetic manipulations to complex word problems. This module will equip you with the essential knowledge and strategies to confidently solve these types of questions.
Understanding Algebraic Expressions
An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y), and operators (like +, -, ×, ÷). It doesn't contain an equals sign, so it doesn't state a complete mathematical sentence.
3a + 4b
Understanding Algebraic Equations
An algebraic equation is a statement that two mathematical expressions are equal. It always contains an equals sign (=) and has a solution (or solutions) that make the statement true.
Visualizing the process of solving a linear equation. Imagine a balance scale. On one side, you have '2x + 5'. On the other, you have '15'. To find 'x', we first remove the '+ 5' from the left side by subtracting 5. To keep the scale balanced, we must also subtract 5 from the right side. Now the scale shows '2x' on one side and '10' on the other. This means two 'x's are equal to 10. To find the value of a single 'x', we divide both sides by 2. This leaves 'x' on one side and '5' on the other, revealing the solution.
Text-based content
Library pages focus on text content
Key Concepts and Strategies for GRE
The GRE often tests your ability to translate word problems into algebraic expressions and equations, and then solve them efficiently. Here are some crucial strategies:
| Concept | GRE Application | Key Strategy |
|---|---|---|
| Translating Words to Algebra | Word problems involving unknown quantities. | Identify keywords (e.g., 'is' means '=', 'of' means '×', 'more than' means '+', 'less than' means '-'). Assign variables to unknown quantities. |
| Solving Systems of Equations | Problems with two or more related unknowns. | Use substitution or elimination methods. Often, you can set up two equations from the problem statement. |
| Inequalities | Problems involving 'greater than' or 'less than'. | Remember to reverse the inequality sign when multiplying or dividing by a negative number. |
| Exponents and Roots | Simplifying expressions with powers and roots. | Master exponent rules (e.g., x^a * x^b = x^(a+b)) and properties of roots. |
Don't get bogged down in complex algebra. For many GRE problems, especially in the Quantitative Comparison section, you can often determine the relationship between quantities without fully solving for the variable. Estimation and strategic substitution can save valuable time.
Practice Problems
The best way to master algebraic expressions and equations is through consistent practice. Work through official GRE practice questions and focus on understanding the underlying logic rather than just memorizing formulas.
y = 2x + 3. Substitute x=4: y = 2(4) + 3 = 8 + 3 = 11.
Learning Resources
Official GRE Math Review from ETS, covering the fundamentals of algebraic expressions and their manipulation.
Official GRE Math Review from ETS, focusing on solving various types of algebraic equations and inequalities.
Comprehensive video lessons and practice exercises covering all fundamental algebra topics, including expressions and equations.
A blog post from Magoosh offering tips and strategies for tackling algebra questions on the GRE.
Kaplan's guide to GRE algebra, providing explanations and practice problems for expressions and equations.
A curated YouTube playlist from GregMat+ covering essential algebra concepts for the GRE with clear explanations.
Blog posts from Manhattan Prep offering in-depth strategies and explanations for GRE algebra topics.
A resource with explanations and practice questions on algebraic expressions and equations for GRE preparation.
A forum discussion and strategy guide on applying algebra to GRE Quantitative Comparison questions.
A foundational explanation of algebraic equations, their history, and basic properties.