Equation Solver

Type an equation and this equation solver finds every solution, shows each step and checks the answer by putting it back into the equation where possible. It handles two-step, absolute value, fraction and quadratic equations.

Tip: use the math keyboard for symbols like √, x² and fractions. You can also attach a photo, screenshot or PDF of the problem (up to 4 files).

Try an example:
Explanation

Math keyboard

Keys go in at the cursor. Select part of your problem first to wrap it — for example, select x + 1 and press √.

How to use the equation calculator

  1. Type the equation with an equals sign, such as “4x − 9 = 11”. The math keyboard below the box is already open for =, | |, powers, roots and fractions.
  2. Got a sheet that says “solve each equation”? Add a photo and Sumzo reads every equation on it.
  3. Press Solve. The solutions come first, then the steps, then a check.
  4. If a step is unclear, ask “Why?” or a follow-up question.

Worked examples

Easy: a two-step equation, 4x−9=114x - 9 = 11

  1. Step 1 — add 9 to both sides: 4x=204x = 20.
  2. Step 2 — divide both sides by 4: x=5x = 5.
  3. Check: 4(5)−9=114(5) - 9 = 11 ✓.

Medium: an absolute value equation, ∣2x−3∣=7|2x - 3| = 7

  1. The expression inside can be 77 or −7-7, so solve two equations.
  2. 2x−3=72x - 3 = 7 gives 2x=102x = 10, so x=5x = 5.
  3. 2x−3=−72x - 3 = -7 gives 2x=−42x = -4, so x=−2x = -2.
  4. Check: ∣2(5)−3∣=∣7∣=7|2(5) - 3| = |7| = 7 ✓ and ∣2(−2)−3∣=∣−7∣=7|2(-2) - 3| = |-7| = 7 ✓.

Hard: fractions on both sides, x+13=x−22\frac{x + 1}{3} = \frac{x - 2}{2}

  1. Multiply both sides by 6 (the lowest common denominator): 2(x+1)=3(x−2)2(x + 1) = 3(x - 2).
  2. Expand: 2x+2=3x−62x + 2 = 3x - 6.
  3. Subtract 2x2x and add 6: x=8x = 8.
  4. Check: 93=3\frac{9}{3} = 3 and 62=3\frac{6}{2} = 3 ✓.

Common mistakes when solving equations

  • Solving only one case of an absolute value equation. ∣2x−3∣=7|2x - 3| = 7 has two solutions, 55 and −2-2.
  • Doing an operation to one side only. Whatever you add, subtract, multiply or divide, do it to both sides.
  • Multiplying only some terms by the common denominator. Every term on both sides must be multiplied.
  • Not checking the answer. Equations with fractions, square roots or absolute values can give a value that doesn’t work, so substitute it back.

Frequently asked questions

What types of equations can the equation solver handle?

Linear and two-step equations, equations with fractions or brackets, absolute value equations, quadratics, and many others such as exponential and trigonometric equations. Linear and quadratic equations are solved and checked exactly by Sumzo’s math engine; others are solved by Sumzo AI.

How do I solve absolute value equations?

Get the absolute value on its own, then split it into two equations: one where the inside equals the positive number and one where it equals the negative number. Solve both and check each solution in the original equation.

How do I solve 2 step equations?

Undo addition or subtraction first, then multiplication or division. For 4x−9=114x - 9 = 11: add 9 to get 4x=204x = 20, then divide by 4 to get x=5x = 5.

Does the equation solver show the steps?

Yes. Each solution shows the working step by step and, where possible, a check that puts the answer back into the equation.

Can it solve several equations at once?

For two or three linear equations that must hold together, use the System of Equations Calculator. For a worksheet of separate equations, add a photo and choose to solve them all.

Is the equation calculator free online?

Yes. It works in your browser on any device, without an account. AI answers have a fair-use daily limit.