Solving a linear equation
Undo the +b first, then undo the ×a. You are peeling the equation back to x.
Algebra Calculator
Solve algebra problems with every step shown — and a proof at the end that the answer is right. Free, no signup, no locked steps.
In short
An algebra calculator solves equations and simplifies expressions step by step. VerifySolve handles linear equations, quadratics and two-equation systems with exact fraction arithmetic — no rounding drift — and shows every move a teacher would write. It then proves each answer by substituting it back into the original problem, so you see both sides balance before you trust the result.
The formulas doing the work
Four ideas cover almost everything this page solves. When you see a step you don't recognise, it is one of these.
Distributive law
The number outside the bracket multiplies everything inside it.
Quadratic formula
Works for every quadratic ax² + bx + c = 0 — even when factoring fails.
Zero-product rule
If two things multiply to zero, at least one of them is zero.
Worked examples — with the proof
Real problems, fully worked. Notice the last line of every card: the answer, checked.
3x + 7 = 22
- 1.Subtract 7 from both sides: 3x = 15
- 2.Divide both sides by 3: x = 5
x = 5
Verified: 3(5) + 7 = 22 ✓
2(x − 3) = 4x + 6
- 1.Expand the bracket: 2x − 6 = 4x + 6
- 2.Subtract 4x from both sides: −2x − 6 = 6
- 3.Add 6 to both sides: −2x = 12
- 4.Divide by −2: x = −6
x = −6
Verified: 2(−6 − 3) = −18 and 4(−6) + 6 = −18 ✓
x² − 5x + 6 = 0
- 1.Factor: (x − 2)(x − 3) = 0
- 2.Set each factor to zero: x − 2 = 0 or x − 3 = 0
x = 2 or x = 3
Verified: 2² − 5(2) + 6 = 0 and 3² − 5(3) + 6 = 0 ✓
x + y = 10, x − y = 4
- 1.Add the equations: 2x = 14, so x = 7
- 2.Substitute x = 7 into x + y = 10: y = 3
x = 7, y = 3
Verified in both: 7 + 3 = 10 and 7 − 3 = 4 ✓
x/3 + 2 = 5
- 1.Subtract 2 from both sides: x/3 = 3
- 2.Multiply both sides by 3: x = 9
x = 9
Verified: 9/3 + 2 = 5 ✓
Common mistakes (and how the proof catches them)
Doing something to one side only
Whatever you do to one side of an equation, you must do to the other. Subtracting 7 from the left of 3x + 7 = 22 but not the right breaks the balance — the equals sign stops being true.
Sign slips when moving terms
A term that crosses the equals sign flips its sign: +5 moved over becomes −5. Most wrong algebra answers are sign slips, not hard math — which is exactly why the plug-back proof matters.
Half-distributing a bracket
2(x − 3) means both terms get multiplied: 2x − 6, not 2x − 3. Forgetting the second term silently changes the problem.
Forgetting the second root
A quadratic usually has two answers. From (x − 2)(x − 3) = 0, the zero-product rule gives x = 2 and x = 3. Stopping at the first root loses half the solution.
Algebra calculator — questions
What can this algebra calculator solve?
Linear equations in one variable (including brackets and fractions like x/3 + 2 = 5), quadratic equations by factoring or the quadratic formula, systems of two linear equations, and simplifying or factoring basic expressions.
How do I type a system of equations?
Type both equations separated by a semicolon — for example "x + y = 10; x - y = 4". You will get elimination steps and a check in both equations.
Why does every answer include a check?
Because an unchecked answer is just a claim. VerifySolve substitutes the solution back into the original problem and shows both sides balancing. That is the proof the answer is right — look for the green Verified card under the steps.
Does it show the steps for free?
Yes — all of the steps, free, with no signup. Many big-name solvers show the first steps and charge for the rest; VerifySolve does not lock any part of the working.
Keep solving
Equation Solver →
One-variable equations of every kind
Quadratic Equation Solver →
Factoring first, the formula when needed — roots verified
System of Equations Calculator →
Elimination and substitution, shown in full
Exponent Calculator →
Powers, exponent rules and exponential equations
Word Problem Solver →
Words into equations, solved in stages
Back to the Solver →
The general math solver with proof on every answer