Learn to see the relationship, not just the answer.
Practice algebra online with free quizzes covering linear equations, inequalities, expressions, variables, and algebraic reasoning. Each quiz includes instant feedback, hints, answers, and clear explanations so you can identify the step that worked—or the step that caused a mistake.
Choose a mixed algebra quiz for a broad review, or focus on a specific skill such as linear equations or inequalities. The quizzes are short enough for regular practice and include explanations that help you review the reasoning behind each answer.
A mixed introduction to equations, expressions, functions, systems, and algebraic reasoning.
Work through one-step and two-step equations, parentheses, and variables on both sides.
Practice equation rules, inequalities, sign changes, and multi-step algebra decisions.
A reliable algebra solution is not a collection of memorized moves. Each step should preserve the mathematical relationship while making the unknown quantity easier to isolate.
Identify the variable, operations, parentheses, equal sign, and any restrictions. Decide what is being done to the unknown before you try to undo it.
Use the distributive property and combine like terms when appropriate. Simplifying an expression changes its form, not its value.
When solving an equation, apply the same valid operation to both sides. The goal is to isolate the variable while preserving equality.
Negative numbers can change the logic of a step. In inequalities, multiplying or dividing by a negative number reverses the inequality sign.
Substitute your answer into the original equation or test it against the original inequality. A quick check catches many sign and arithmetic mistakes.
The equal sign means the expression on the left has the same value as the expression on the right. Solving an equation means changing both expressions in a way that keeps that equality true.
Consider the equation 4x − 9 = 23. The variable is multiplied by 4 and then 9 is subtracted. Undo those operations in reverse order.
When reviewing a missed question, find the first incorrect decision. That tells you whether the problem was arithmetic, sign handling, distribution, or equation logic.
A factor outside parentheses multiplies every term inside. Missing one term changes the expression and usually sends the rest of the solution in the wrong direction.
Terms can be combined only when their variable parts match. Coefficients change; exponents and variable structure do not disappear.
Multiplying or dividing both sides by a negative number changes the order relationship, so the inequality symbol must point the other way.
Word problems become easier when you separate the situation from the calculation. First choose what the variable represents, then convert each relationship into mathematical language.
You do not need to take every quiz in the same order. The best starting point depends on whether your difficulty is broad algebra fluency, equation mechanics, or inequality rules.
Use a mixed set when you want several kinds of algebra in one session and a quick picture of which skills deserve more attention.
Start Algebra QuizzesFocus on inverse operations, parentheses, variables on both sides, and checking solutions by substitution.
Practice Linear EquationsPractice the difference between equality and comparison, especially the sign reversal that occurs with negative multiplication or division.
Practice Equations & InequalitiesShort explanations for rules that often cause mistakes even when the arithmetic itself is easy.
You should be comfortable with the four basic operations, negative numbers, fractions, decimals, and order of operations. Algebra uses those arithmetic skills while adding variables and relationships.
An expression is a mathematical phrase such as 3x + 5. An equation states that two expressions are equal, such as 3x + 5 = 20. Expressions can be simplified or evaluated; equations can be solved for unknown values.
An equation states that two quantities are equal. Applying the same valid operation to both sides preserves that equality, which is why the balance idea is central to solving equations.
The inequality sign reverses when both sides are multiplied or divided by a negative number. This keeps the comparison true. For example, from -2x > 6 we obtain x < -3.
Substitute the value back into the original equation or inequality. For an equation, both sides should produce the same result. Checking the original problem is more reliable than checking only your last line of work.
Try the problem on your own first. If you are stuck, use the hint as a small prompt rather than as a shortcut. After answering, read the explanation and identify the step that made the solution work.
Use the explanation after each question to compare your reasoning with the intended method. A correct answer matters, but understanding why the step works is what makes the skill reusable.