GMAT Linear Equations: A Guide to Logical Problem Solving

Linear equations on the GMAT are a test of logic as much as algebra. Success isn't just about finding 'x'; it's about efficiently translating complex scenarios and determining sufficiency. This guided path will teach you the core algebraic methods and the critical reasoning skills needed for a top GMAT Quant score.

Section 1: The Core Algebraic Engine

Building the Foundation: Solving for a Variable

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Start by reinforcing the fundamental skill of isolating a variable. Our interactive balancer visually demonstrates the step-by-step process of solving any linear equation.

Step 1The Equation

$$ 3x + 5 = 17 $$

Goal: Isolate x.

Step 2Step 1: Subtract 5

Subtract 5 from both sides to remove the constant.

$$ 3x = 17 - 5 $$

$$ 3x = 12 $$

Step 3Step 2: Divide by 3

Divide both sides by 3 to isolate x.

$$ x = \frac{12}{3} $$

$$ x = 4 $$

Core Methods: Solving Systems of Equations

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Learn the two essential algebraic methods—Substitution and Elimination—for finding a unique solution when you have two variables and two equations.

Step 1The System

$$ x + y = 10 $$
$$ x - y = 2 $$

Step 21. Isolate Variable

From Eq 1: $$ x = 10 - y $$

Step 32. Substitute

Plug into Eq 2:
$$ (10 - y) - y = 2 $$
$$ 10 - 2y = 2 $$

Step 43. Solve

$$ 8 = 2y \implies y = 4 $$
$$ x = 10 - 4 = 6 $$
Solution: (6, 4)

1Tab 1 of 2•Substitution Method

Section 2: GMAT-Specific Strategies & Applications

The Art of Translation: Simple Word Problems

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The GMAT loves word problems. This interactive guide teaches the crucial first step: deconstructing a problem statement and translating it into a solvable equation.

Interactive Sentence Translator

A number is doubled and then increased by 7. The result is 25.

Equation Build-Up

$$ 2x $$

Application: Advanced Word Problems

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Move on to more complex GMAT-style scenarios (like age or mixture problems) that require you to build and solve a complete system of two equations.

Systems of Equations: Word Problems

The sum of the present ages of a father and his son is 60 years. Six years ago, the father's age was five times the age of the son. What is the son's present age?

Equation Build-Up

$$ F + S = 60 $$

The Logic of Data Sufficiency

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Master the most unique GMAT question type. Learn to analyze equations for sufficiency without needing to solve them, saving valuable time and avoiding common traps.