This free solve for x calculator finds the value of x in any linear equation and shows every step, from expanding brackets to checking the answer. It also handles fractions, decimals, inequalities, quadratics, rational equations and formulas where you need to solve for y or another letter. Type the equation above, or tap an example to see how it works. For everyday sums with trig, logs and fractions, use the free CalcSolver scientific calculator.
In short: Type an equation with an equals sign, choose the letter to solve for, and press Solve. You get the exact answer, a decimal where it helps, a numbered step-by-step solution, a graph and an automatic check.
In this guide
How to Use the Solve for x Calculator
- Type your equation in the box, for example
3(x + 2) − 4 = 2x + 9. Use the symbol keys if your keyboard has no ² or ≤. - Pick the letter to solve for. The calculator lists every letter in your equation and picks x when it is there.
- Press Solve, or just keep typing. The answer updates as you go.
- Read the steps. Each step says what was done and why, in the same order you would write it in your notebook.
- Copy or share the answer, the full steps or a link that reopens the same equation.
What This Calculator Can Solve
Most free equation solvers stop at simple linear equations or hide the steps. This one covers the equation types students meet from pre-algebra to algebra 2, with the full working shown for each.
| Equation type | Example | What you get |
|---|---|---|
| One-step and two-step equations | 4x − 7 = 21 | x = 7, with each inverse operation shown |
| Multi-step, x on both sides | 3(x + 2) − 4 = 2x + 9 | Expand, collect, move terms, divide |
| Fractions and decimals | x/2 + x/3 = 10 | Clears fractions with the lowest common denominator |
| Linear inequalities | −2x + 5 > 11 | x < −3, interval notation and the sign-flip rule |
| Solve for y or any letter | 2x + 3y = 12 | y = −(2/3)x + 4 |
| Formulas (literal equations) | A = (1/2)bh, solve for h | h = 2A / b |
| Quadratic equations | x² − 5x + 6 = 0 | Discriminant, quadratic formula, factored form |
| Rational equations | 3/x + 1 = 2 | Restrictions, cross-multiplying, extraneous roots removed |
| No solution or every number | 2(x + 3) = 2x + 5 | Explains why no value of x works |
In short: One box solves linear equations, inequalities, formulas, quadratics and rational equations, and always shows why each step is allowed.
How to Type Your Equation
| To write | Type | Example |
|---|---|---|
| Multiplication | Nothing, *, or × | 3x, 2(x + 1), 4 * x |
| Division or a fraction | / | x/4, (2x − 1)/3 |
| Powers | ^ or ² | x^2 or x² |
| Negative numbers | − | −2x + 5 |
| Brackets | ( ) | 3(x − 4) |
| Inequalities | <, >, <=, >= or ≤, ≥ | 3x − 4 ≤ 2x + 1 |
| Decimals | . (point) | 0.4x + 1.2 = 3.6 |
Two details matter. First, 1/2x means (1/2)·x, read left to right. If you mean 1 over 2x, type 1/(2x). Second, letters are case-sensitive, so A and a are different variables, which keeps science formulas correct.
How the Calculator Solves for x
It follows the same balance method a teacher would. Every step does the same thing to both sides, so the equation stays true.
- Expand brackets and combine like terms on each side.
- Clear fractions by multiplying every term by the lowest common denominator.
- Move the x terms to one side. If the right side has the bigger x term, it swaps the sides first so x stays positive.
- Move the other terms to the other side.
- Divide by the coefficient of x. For an inequality, dividing by a negative number flips the sign.
- Check the answer by putting it back into the original equation.
The arithmetic uses exact fractions, so 0.1 + 0.2 is treated as exactly 3/10 and answers like x = 2/3 are not rounded to 0.6666667. The full method, with practice, is in our guide on how to solve for x.
In short: Expand, clear fractions, gather x on one side, move the numbers, divide, then check. The calculator writes out each of these steps for you.
Worked Examples
A two-step equation
Example: 4x − 7 = 21 → add 7 to both sides: 4x = 28 → divide by 4: x = 7. Check: 4 × 7 − 7 = 21.
An inequality where the sign flips
Example: −2x + 5 > 11 → subtract 5: −2x > 6 → divide by −2 and flip the sign: x < −3. Test x = −4: −2(−4) + 5 = 13, and 13 > 11 is true.
The flip happens because multiplying or dividing both sides by a negative number reverses the order of the numbers. For example, 2 < 3, but −2 > −3.
Solve for y in terms of x
Example: 2x + 3y = 12 → subtract 2x from both sides: 3y = 12 − 2x → divide by 3: y = 4 − (2/3)x. This is the slope-intercept form, with slope −2/3 and y-intercept 4.
A rational equation with an extraneous root
Example: (x² − 1)/(x − 1) = 2 → x cannot be 1 → cross-multiply: x² − 1 = 2x − 2 → x² − 2x + 1 = 0 → x = 1. But x = 1 makes the denominator 0, so it is rejected: no solution.
An extraneous root is an answer that the algebra produces but the original equation does not allow. Many solvers print it anyway. This one checks each root against the denominators and tells you which ones to throw out.
How to Solve for x on a Scientific or Graphing Calculator
Some handheld calculators can solve an equation numerically. They give a decimal answer but no steps, so they are best for checking your work.
Casio scientific calculators (fx-991ES PLUS, fx-115ES PLUS and similar)
- Work in COMP (calculate) mode.
- Type the equation. Press ALPHA then X for the letter x, and ALPHA then the CALC key for the equals sign.
- Press SHIFT then CALC to start SOLVE.
- Enter a starting guess for X and press =. The calculator shows a solution.
Casio notes that SOLVE uses Newton’s method, so it returns only one solution even when there are more, and it can fail if the starting guess is far away. Steps differ slightly between models.
TI-84 Plus CE
- Press MATH, then choose B:Solver.
- In MathPrint mode, type the left side in E1 and the right side in E2, pressing ENTER after each.
- Move to x and press ALPHA then SOLVE (the ENTER key).
In Classic mode, you enter the equation as 0 = left side − right side instead. Like the Casio, the TI solver gives one numeric answer and no working.
Common Input Mistakes
- Forgetting the equals sign. Without =, the calculator simplifies the expression instead of solving it.
- Missing brackets. 2x + 1/3 is not the same as (2x + 1)/3. Put brackets around a whole numerator or denominator.
- Using x as a times sign. Use * or × for multiplication, because x is read as a letter.
- Typing a comma in a number. Write 1200, not 1,200. A comma is read as a decimal point.
- Two equals signs. Solve one equation at a time.
Practice Problems (With Answers)
Solve each one by hand, then type it into the calculator to check your steps.
1. 9x − 4 = 23
x = 3. Add 4 to get 9x = 27, then divide by 9.
2. 5(x − 2) = 3x + 6
x = 8. Expand to 5x − 10 = 3x + 6, so 2x = 16.
3. x/3 − 1 = x/4
x = 12. Multiply every term by 12: 4x − 12 = 3x.
4. 4 − 3x ≥ 10
x ≤ −2. Subtract 4 to get −3x ≥ 6, then divide by −3 and flip the sign.
5. Solve P = 2l + 2w for w
w = (P − 2l)/2, which is the same as (1/2)P − l. Subtract 2l, then divide by 2.
6. x² + x − 12 = 0
x = −4 or x = 3. It factors as (x + 4)(x − 3) = 0.
Solve for x Calculator: Frequently Asked Questions
Is this solve for x calculator free, with steps?
Yes. Every feature is free, including the full step-by-step solution, the graph and the answer check. There is no sign-up and no limit on how many equations you solve.
Can it solve for y or another letter?
Yes. Choose the letter in the Solve for menu. The calculator treats every other letter as a number, so it can rearrange formulas such as y = mx + b for m, or A = (1/2)bh for h.
Does it solve inequalities?
Yes. It solves linear inequalities and quadratic inequalities, flips the sign when you divide by a negative number, and gives the answer in interval notation, for example (−∞, −3).
Can it solve quadratic equations?
Yes. It writes the equation in standard form, works out the discriminant, uses the quadratic formula and gives exact answers with square roots, plus decimals. If the discriminant is negative, it says there is no real solution.
What does “no solution” mean?
It means the x terms cancel and leave a false statement, such as 6 = 5, so no value of x can work. If they cancel and leave a true statement, such as 0 = 0, every number is a solution.
How do I solve for x on a calculator?
On many Casio models, type the equation, then press SHIFT and CALC to use SOLVE. On a TI-84 Plus CE, press MATH and choose Solver. Both give one decimal answer without steps, so use this page when you need the working.
Is my equation saved or sent anywhere?
No. The calculator runs entirely in your browser. Your equation is not sent to a server or stored. The only place it appears is in the page address, so you can share it.
Sources
- Casio, fx-570ES PLUS / fx-991ES PLUS User’s Guide: Using SOLVE.
- Texas Instruments, How do I use the Solver on the TI-84 Plus CE?
- OpenStax, Elementary Algebra 2e, Section 2.7: Solve Linear Inequalities, Rice University.
Keep learning: how to solve for x by hand, simplifying algebraic expressions, functions and f(x), or the full algebra guides. For everyday sums, use the CalcSolver scientific calculator.