Algebra Summary

GRE Quantitative · Axiom Academy

Key takeaways from Unit 3 — equations, functions, and the algebra skills the rest of the GRE Quant section leans on. Every equation and inequality you solved comes down to the same move: isolate the variable with inverse operations — and flip the inequality sign whenever you multiply or divide by a negative. The quadratic formula solves every quadratic, but factoring is faster when the numbers cooperate — check the discriminant to know how many real solutions to expect before you start. A system of two linear equations has exactly one solution where the lines cross — substitution and elimination are two paths to the same intersection point. Function notation, exponent rules, and coordinate geometry (slope, distance, midpoint) are the toolkit — they show up constantly inside word problems, not just as standalone questions. Word problems and business/finance questions are algebra with a translation step : name the unknown, turn each sentence into an equation, then solve exactly as you practiced. Core Concept Linear Equations & Inequalities Solving a linear equation means undoing the operations applied to the variable, one at a time, in reverse order. Inequalities work the same way — with one twist: multiplying or dividing by a negative number reverses the inequality sign. When to use: any "solve for x " problem with the variable to the first power Watch out for: forgetting to flip the sign on Core Concept Quadratic Equations

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