5x − 3 = 2x + 9
- 1.Subtract 2x from both sides: 3x − 3 = 9
- 2.Add 3 to both sides: 3x = 12
- 3.Divide by 3
x = 4
Verified: 5(4) − 3 = 17 and 2(4) + 9 = 17 ✓.
Solve for x — every undo shown, answer proven
Type the equation and watch x get isolated one inverse operation at a time — then the answer is plugged back into your original equation to prove it balances. No guessing, no skipped steps.
Covered: linear and quadratic equations in one unknown, x. Literal equations (rearranging a formula for a letter) and equations with square roots are not covered yet — the solver will say so rather than guess.
- ✓100% free — no paywall, ever
- ✓No sign-up, no app
- ✓Every answer verified before you see it
In short
“Solve for x” means isolating x on one side of an equation using inverse operations: undo addition with subtraction, multiplication with division, and squares with roots. VerifySolve performs those moves in order, keeps answers as exact fractions, and then substitutes the value back into your original equation to prove both sides come out identical.
Isolating x, in formulas
Every “solve for x” problem is one of these shapes underneath. Learn to see the shape and the undo sequence writes itself.
One step: x + b = c
Two steps: ax + b = c
Fraction form: x/a = c
Quadratic: x² = c
Worked examples — undone step by step
From one step to brackets to two-sided equations — the undo order is the lesson. Run any of them in the solver to see the same steps live.
x/3 + 2 = 5
- 1.Subtract 2: x/3 = 3
- 2.Multiply both sides by 3
x = 9
Verified: 9/3 + 2 = 5 ✓. Fraction coefficients stay exact throughout.
4(x + 1) = 2x + 10
- 1.Expand the bracket: 4x + 4 = 2x + 10
- 2.Subtract 2x and 4: 2x = 6
- 3.Divide by 2
x = 3
Verified: 4(3 + 1) = 16 and 2(3) + 10 = 16 ✓.
7 − 2x = 3
- 1.Subtract 7: −2x = −4
- 2.Divide by −2 (signs flip together)
x = 2
Verified: 7 − 2(2) = 3 ✓. Negative coefficients are where most sign errors happen — the plug-back check catches them.
Common mistakes — and how to dodge them
Undoing in the wrong order
For 2x + 3 = 11, undo the +3 before dividing by 2. Undoing in the order things were built — last on, first off — is the entire method. Dividing first gives (x + 3)/… a mess that leads nowhere clean.
Forgetting the negative root
x² = 16 has two solutions. Writing only x = 4 loses half the answer — and on tests, often the mark. Whenever you undo a square, write ± before the root.
Dividing by a negative and keeping the sign
−2x = −4 means x = 2, not −2: negative divided by negative is positive. This exact slip is why the verification step exists — plug your answer back and the error announces itself.
Solve for X Calculator — questions
How do you solve for x?
Undo everything that was done to x, in reverse order, using inverse operations on both sides: undo addition with subtraction, multiplication with division. The calculator shows each undo as a named step, then verifies the final value by substituting it back into the original equation.
What kinds of “solve for x” problems are covered?
One-step and multi-step linear equations, equations with brackets, fractions and decimals, x on both sides, and quadratic equations in x (which give two values). Answers are exact fractions.
Can it solve for a different letter, like solving d = rt for t?
Not yet — that is called a literal equation (rearranging a formula), and it is a different skill the engine does not cover yet. For distance-rate-time problems specifically, try our staged word problem solver, which builds and solves d = rt problems for you.
Why do some equations have two answers for x?
Quadratic equations do: x² = 16 means x = 4 or x = −4, because both square to 16. The solver always reports both roots and verifies each one separately.
What if x appears under a square root or in an exponent?
Square-root equations are not covered yet. Some exponential equations are — when both sides can be written as powers of the same base, our exponent calculator solves them exactly. If a problem is out of scope, the solver tells you instead of guessing.
Is the solve for x calculator free?
Yes — completely free, no sign-up, no app, and every step (including the verification) is shown in full.
Keep solving
Equation Solver →
Any equation — linear, quadratic or system — routed automatically.
Algebra Calculator →
The all-rounder with the same verified engine.
System of Equations Calculator →
When there are two unknowns, x and y, in two equations.
Word Problems →
Stories that become solve-for-x equations — set up and solved in stages.
A note on honest use: VerifySolve is built for learning. Use the steps to understand the method, then close the tab and try one on your own — that is where the grade actually comes from. If your teacher or school has a policy on calculators, follow it.