GMAT® Algebra - The Comprehensive Course |Learn from scratch

Learn how to solve equations by equating left and right sides and applying the same operations on both sides, including addition, subtraction, multiplication, division, distribution, factoring, and squaring.

Learn to solve a set of linear equations by elimination or substitution, treating each equation as a line and finding its intersection, while isolating x and y.

Learn how combining equations solves linear systems, using x+y=1 and x−y=1 to show equality persists under addition and subtraction, yielding x=1 and y=0.

Solve and simplify algebraic expressions from practice test 1, applying exponent rules, factoring, and common-base techniques to reach concise, correct answers.

Identify the roots of a quadratic expression by locating where its graph intersects the x-axis, giving the solutions, with no real roots when the graph never crosses the axis.

Learn to factor quadratic expressions by methods—factorization and the quadratic formula—classify by a=1 or a≠1, factor into numbers summing to b, then set each factor to zero to find roots.

Reinforce factorization techniques for expressions with multiple variables, guiding you through breaking expressions into factors, solving for x, and embracing abstraction through focused practice.

Explore the concept of functions by distinguishing independent and dependent variables, mastering function notation f(x), and evaluating functions through substitution and input examples.

Explore composing functions by substituting g(x) into f(x), expanding the result, and evaluating f(g(1)) using f(x)=x+1 and g(x)=x+5.

Study inequalities by contrasting linear and quadratic cases, and master manipulation rules: add or subtract on sides, multiply or divide by positives, flipping with negatives when the sign is unknown.

Explore how to solve quadratic inequalities by factoring, locating roots on a number line, and testing representative values to identify valid intervals.

Learn to factor quadratic expressions, determine solution sets for inequalities, and interpret boundary points on the number line.

Explore how absolute values measure distance, solve inequalities, and express solution sets as unions on the number line.

Learn to solve absolute value inequalities involving quadratic expressions by splitting into cases, analyzing signs, and finding intersecting solution sets on the number line.

Explore how exponents interact with inequalities: when the base is greater than one, exponents yield larger values; when the base is between zero and one, exponents yield smaller values.

Determine the domain of x for root expressions by ensuring the radicand is nonnegative, then solve root-based inequalities by isolating the root, squaring, and testing intervals, including boundary values.

Master arithmetic progressions, where consecutive terms differ by a constant d and the nth term is a + (n-1)d. Note geometric progressions use a constant multiple.

Explore problem-solving strategies for algebra through Practice Test #2, covering sequences, ratios, direct proportionality, arithmetic and geometric progressions, and practical GMAT-style word problems with algebraic manipulation.

Solve data-sufficiency based GMAT algebra problems by analyzing x and y real numbers, using statement evaluation, case analysis, and value-plugging to determine relationships like x>y and expressions with absolute values.

This tutorial for GMAT algebra Practice Quiz IV demonstrates data-sufficiency reasoning, combining statements, and handling cube roots and absolute values to compare x, y, z.

Enhance data sufficiency skills for GMAT algebra through practice on x, y, and z relationships and absolute value problems. Learn pattern recognition to solve quiz questions efficiently.

Analyze practice quiz questions on statement sufficiency in GMAT algebra, including inequalities, not negative and not positive reasoning, progression rules, and an absolute-value inequality.

Analyze practice quiz problems for gmat algebra, covering arithmetic progression and common difference, statement sufficiency, and solving inequalities and quadratics using discriminant and absolute value cases.

Solve practice GMAT algebra questions by analyzing statement sufficiency, absolute value inequalities, and quadratic relations to determine x and y, with stepwise reasoning and test-taking strategies.

Explore solving GMAT algebra questions through practice quizzes, focusing on arithmetic progressions, statement sufficiency, and substitution techniques to determine x, y, and z.

Practice quiz tutorial on solving GMAT algebra problems, focusing on data sufficiency with inequalities, translating word problems into algebra, and working with quadratic expressions.