Algebra is the language every later course is written in. These guides explain each core technique, show where students usually slip, and walk through examples you can check step by step.
Most algebra problems come down to one idea: perform the same legal operation on both sides until the unknown is isolated, or rewrite an expression into an equivalent form that is easier to work with. The guides in this section take that idea through every common problem type, from one-step linear equations to quadratics that need the quadratic formula.
Each article starts with the reason a method works, then gives worked examples with every intermediate line shown, a list of the mistakes teachers mark most often, and a quick way to check the final answer. When you want to compare your own working, the matching calculator shows the same steps.
Every example on these pages has been checked by substituting the answer back into the original problem, and the same habit is the single best way to protect your own marks: a solution that does not satisfy the original equation is not a solution, however tidy the working looks.
If you are new to the topic, start with linear equations, then simplifying expressions and factoring, because quadratics, systems and inequalities all reuse those skills.
Algebra
A linear equation is solved by undoing what has been done to the unknown, in reverse order, while keeping both sides equal. This guide turns that idea into a five-step routine and works through every common variation.
Algebra
Factoring is fastest when it works, completing the square explains where the formula comes from, and the quadratic formula always works. Here is how to choose, with every example checked.
Algebra
Factoring is multiplication in reverse. Work through a fixed checklist, starting with the greatest common factor, and almost every polynomial you meet in algebra can be broken into simple factors.
Algebra
A system of equations asks for values that satisfy every equation at once. Substitution and elimination both work for any linear system; the art is choosing the one that needs less arithmetic.
Algebra
Simplifying means rewriting an expression in an equivalent, shorter form without changing its value for any allowed input. A handful of rules, applied in a sensible order, covers almost every case.
Algebra
Inequalities are solved almost exactly like equations, with one extra rule and a different kind of answer: a range of values instead of a single number. This guide covers every common type.
Algebra
Completing the square rewrites $x^2 + bx$ as a perfect square minus a constant. It solves any quadratic, gives the vertex of a parabola, produces the quadratic formula, and reappears in circles and calculus.