Free algebra practice with explanations

Algebra Problems with Step-by-Step Solutions

Practice algebra from easy exercises to super hard challenges. Work through equations, questions, tests, and worksheets with hints, answers, and clear step-by-step explanations.

Free practice No registration Step-by-step solutions Multiple difficulty levels
6 problem levels
4 practice formats
8 worksheet topics
0 signups needed
A better way to practice

Practice algebra with a clear goal

Algebra becomes easier when practice is organized around one difficulty level or one type of problem. Instead of jumping between unrelated exercises, choose a problem set that matches what you want to improve and work through several similar examples.

Start at the right difficulty

Easy and intermediate problems are useful for reviewing algebraic rules and building accuracy. Hard, super hard, and advanced sets require more planning, pattern recognition, and multi-step reasoning. Moving up gradually makes it easier to see which methods you already understand and which ones need more practice.

Choose a difficulty

Focus on one algebra skill

If equations are causing trouble, practice equations before returning to mixed problem sets. Focused practice helps you notice repeated structures, such as moving terms, combining like terms, working with absolute value, or checking restrictions before accepting an answer.

Practice equations

Review the reasoning, not only the answer

A correct final answer does not always mean the method is reliable. After solving a problem, compare your steps with the explanation and look for a shorter or clearer approach. The goal is to understand why each transformation is valid so the same idea can be used on a new problem.

See worked examples
What you can practice

From basic equations to advanced algebra reasoning

The problem library is organized for different kinds of algebra practice. Some pages concentrate on short equations and direct calculations, while others use identities, systems, functions, parameters, and several algebraic ideas in the same problem.

Students reviewing the basics can begin with easy algebra problems or Pre-Algebra. More experienced learners can move to hard algebra problems, advanced algebra, or the College Algebra section.

The practice section is useful when you do not want to follow a fixed topic. Take an algebra practice test, answer a set of algebra questions, or open a random algebra problem for a quick challenge.

There is no registration requirement. You can move between problem sets, repeat practice, and review explanations at your own pace.

Step-by-step examples

Learn the method, then solve similar problems

Worked examples show the reasoning behind each answer so you can apply the same method to new algebra problems.

View all algebra equations
Algebraic expressions Hard

If a + b = 7 and ab = 10, find a² + b².

  1. Use the identity: (a + b)² = a² + 2ab + b².
  2. Substitute the known values: 7² = a² + 2 · 10 + b².
  3. So 49 = a² + b² + 20.
  4. Subtract 20 from both sides.
Correct answer: a² + b² = 29
Systems of equations Advanced

Solve the system x + y = 6 and x² + y² = 20.

  1. Square the first equation: (x + y)² = 36.
  2. This gives x² + 2xy + y² = 36.
  3. Substitute x² + y² = 20, so 20 + 2xy = 36.
  4. Then xy = 8. The numbers x and y have sum 6 and product 8.
  5. They are roots of t² − 6t + 8 = 0.
Correct answer: (x, y) = (2, 4) or (4, 2)
Quadratics College

For what values of k does x² − kx + 9 = 0 have one repeated root?

  1. A quadratic has one repeated root when its discriminant equals zero.
  2. For ax² + bx + c, the discriminant is b² − 4ac.
  3. Here, a = 1, b = −k, and c = 9.
  4. So the discriminant is k² − 36.
  5. Set k² − 36 = 0 and solve.
Correct answer: k = 6 or k = −6
Learning from mistakes

What to do when an algebra answer is wrong

Wrong answers are useful when you identify the exact step that caused the problem. Most algebra mistakes come from a small number of habits, and those habits can be corrected with focused review.

Check signs and basic operations

A negative sign, an incorrect distribution step, or a small arithmetic error can change the entire result. Before starting over, scan the work line by line and verify each operation.

Ask whether the same operation was applied to both sides

In an equation, balance matters. Adding, subtracting, multiplying, or dividing on only one side usually creates an invalid equation. Rewrite the step clearly if the transformation is difficult to follow.

Check restrictions and rejected solutions

Rational, radical, logarithmic, and absolute value problems may need extra checks. A value produced during algebraic manipulation is not always valid in the original expression.

Solve a similar problem immediately

Reading a solution can feel clear even when the method is not fully learned. The best check is to close the explanation and solve a similar problem using the same idea on your own.

Interactive algebra question

Try one algebra problem now

Choose an answer, check the result instantly, and review the explanation.

If 2x − 3 = 11, what is the value of x?

Explanation: Add 3 to both sides: 2x = 14. Divide by 2, so x = 7.
Algebra worksheets

Practice with focused algebra worksheets

Choose a worksheet topic and work through equations and expressions step by step.

View all algebra worksheets

Linear Equations Worksheet

Practice solving linear equations with a focused worksheet and answer support.

Open worksheet

Literal Equations Worksheet

Rearrange formulas and solve literal equations for a selected variable.

Open worksheet

One-Step Equations Worksheet

Build speed and accuracy with one-step algebra equations.

Open worksheet
Using worksheets and level pages

Build regular algebra practice without making it complicated

You do not need to complete every page in order. Use worksheets for repeated practice on one skill, level pages for broader course review, and mixed problem sets when you want to test whether you can choose the correct method without being told which rule to use.

Use worksheets for repetition

A focused worksheet is useful when a method still feels slow or inconsistent. Repeating linear equations, literal equations, equivalent expressions, or one-step equations helps make the basic transformations more automatic.

Browse worksheets

Use level pages for broader review

Pre-Algebra, Algebra 1, Algebra 2, and College Algebra cover different ranges of skills. A level page is a practical starting point when you want practice that matches a course rather than a single keyword or equation type.

Choose a level

Return to mixed problems

Topic practice teaches a method; mixed practice checks whether you can recognize when to use it. After reviewing a weak area, return to questions, tests, or random problems and see whether the same mistake appears again.

Open practice tools
FAQ

Common questions about algebra practice

Learn how to use the problem sets, tests, and worksheets on Algebra Problems.

Are the algebra problems free?

Yes. Algebra Problems provides free practice pages, questions, tests, equations, and worksheets without requiring registration.

Where should I start?

Start with easy or intermediate algebra problems if you are reviewing the basics. Move to hard, advanced, or super hard problems when you want more challenging practice.

Do the problems include solutions?

Problem pages are designed around answers, hints, and clear step-by-step explanations so you can review the method after solving a problem.

Can I practice by algebra level?

Yes. The Levels section organizes practice into Pre-Algebra, Algebra 1, Algebra 2, and College Algebra.

Start practicing algebra now

Choose your difficulty level, take an algebra practice test, or get a random algebra problem to solve.

Start practice