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Equation Solver

Solve an equation with one unknown, such as 3(x − 2) + 4 = 2x + 7, with every step shown: multiply out, gather terms, get x alone and check.

Level: Grades 7–8

  • Common Core standard 8.EE.C.7.bSolve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
  • Common Core standard 8.EE.C.7.aGive examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
  • Common Core standard 7.EE.B.4.aSolve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
Printable worksheet

Equation Solver

Inputs

One unknown and one equals sign, for example 5x - 3 = 2x + 9 or (y + 4)/3 = 2y - 1. Brackets, fractions and decimals are fine.

Result

Solution

x = 9

3(x - 2) + 4 = 2x + 7 simplifies to x = 9. x = 9.

x as a decimal
9
Simplified form
x = 9
Type of equation
One solution

See the step-by-step solution ↓

Step-by-step solution

  1. Start with the equation as you typed it

    3(x - 2) + 4 = 2x + 7

  2. Tidy up each side: multiply out any brackets, then combine terms of the same kind, such as the x terms and the plain numbers

    3x − 2 = 2x + 7

  3. Subtract 2x from both sides. That gathers every x on the left and keeps the two sides equal

    x − 2 = 7

  4. Add 2 to both sides. That moves the plain numbers to the right

    x = 9

  5. Check your answer: put x = 9 back into each side of the original equation. Both sides come out the same

    left = 25, right = 25

  6. So the solution is

    x = 9

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Type in an equation and get the answer, with every step explained. This solver handles linear equations with one unknown, such as 5x − 3 = 2x + 9, (y + 4)/3 = 2y − 1 or 0.5t + 1.25 = 3. "Linear" means the unknown is never squared or raised to a higher power. Solving means finding the value that makes both sides equal. The method is always the same: do the same thing to both sides until the unknown stands alone.

The solver works through it the way a teacher would on the board. It multiplies out brackets and combines terms of the same kind. It clears fractions or decimals by multiplying both sides by one number. Then it gathers the unknown on one side and the plain numbers on the other, and divides by the number in front of the unknown. Last, it puts the answer back in to check it.

All the math is exact, so 1/3 stays 1/3 instead of turning into 0.333333. The solver also spots two special cases. Some equations are never true, so they have no solution. Others are always true, so every value works.

Where it's used

Why this math matters outside the classroom:

  • Comparing phone plans. A $20 plan plus $0.10 a minute costs the same as a $35 flat plan when 20 + 0.1m = 35, which is at 150 minutes.
  • Fundraiser break-even. A class selling $8 tickets to cover $120 of costs solves 8t − 120 = 0 and needs to sell 15 tickets.
  • Temperature conversion. Finding the Celsius value of 95°F means solving 95 = 1.8C + 32, which gives C = 35.
  • Fencing a yard. A rectangle 3 m longer than it is wide with a 46 m perimeter gives 2w + 2(w + 3) = 46, so it is 10 m wide.
  • Savings goals. Someone with $150 saved who adds $25 a week reaches $500 when 150 + 25w = 500, after 14 weeks.

Grade level and standards: Grades 7–8; Common Core State Standards for Mathematics 8.EE.C.7.b, 8.EE.C.7.a, 7.EE.B.4.a. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Type the equation with one equals sign, for example 3(x - 2) + 4 = 2x + 7. For multiplication, use * or write the terms side by side (3x, 3(x + 1)). Use / for division and ^ for powers.
  2. Use any single letter as the unknown: x, y, t or n all work. Decimals and fractions such as x/4 or (x + 1)/3 are fine.
  3. Read the solution at the top. When the decimal and fraction forms differ, both are shown underneath.
  4. Open the working to follow each step. The last step is a check: both sides of your original equation are worked out using the answer.

What the inputs mean

Equation
One unknown and one equals sign. To multiply, write 2x or 2(x + 3). If the unknown is on the bottom of a fraction, as in 1/x = 2, multiply both sides by that bottom part first. If the equation turns out to have x² or a higher power, the solver points you to the quadratic equation or polynomial factoring calculator.

Formula and method

a·x + b = c·x + d
(a − c)·x = d − b
x = (d − b) ÷ (a − c),  when a ≠ c
a = c and b = d  →  infinitely many solutions
a = c and b ≠ d  →  no solution

In the formulas, x is the unknown you're solving for. The letters a and c are the numbers in front of x on the left and right sides. The letters b and d are the plain numbers on each side. Any linear equation, however it's written, can be tidied into the form a·x + b = c·x + d.

Next, take c·x and b away from both sides. Doing the same thing to both sides keeps the equation balanced, and it leaves (a − c)·x = d − b. Dividing both sides by a − c leaves x on its own.

If a and c are equal, the x terms cancel out completely. What's left is a statement about plain numbers. If it's true, such as 6 = 6, every value of x works in the original equation. If it's false, such as 6 = 5, no value does.

Fractions and decimals are cleared first. The solver multiplies both sides by the smallest number that turns every fraction or decimal into a whole number. That number is called the least common denominator. The solver keeps exact fractions the whole way through, which is why its check always gives two identical values.

Worked example

Solve 3(x − 2) + 4 = 2x + 7.

  1. Multiply out the bracket and combine the plain numbers on the left: 3x − 6 + 4 = 3x − 2. So the equation is 3x − 2 = 2x + 7.
  2. Subtract 2x from both sides: x − 2 = 7.
  3. Add 2 to both sides: x = 9.
  4. Check: the left side is 3(9 − 2) + 4 = 25 and the right side is 2 × 9 + 7 = 25. They match.

Result: x = 9.

Understanding the result

A single answer such as x = 9 means exactly one value balances the equation. If you drew each side as a line on a graph, this is the x value where the two lines cross.

No solution means the two sides are parallel lines that never meet. Infinitely many solutions means both sides are the same line, written two different ways.

When the answer is a fraction, it's shown in lowest terms, with its decimal value too. If you typed the equation with decimals and the answer's decimal ends (it doesn't repeat forever), the answer is shown as a decimal.

Assumptions and limitations

  • There's exactly one unknown, written as a single letter. Once both sides are tidied up, it's never squared or raised to a higher power.
  • The numbers in the equation are whole numbers, fractions or decimals. They're handled exactly, with no rounding.
  • It doesn't solve equations with x² or higher powers. It also doesn't handle the unknown inside a function, a square root or the bottom of a fraction, or equations with π or e.
  • Systems with two or more unknowns need the system of equations solver.
  • Absolute value equations such as |x − 3| = 5 aren't supported.

Frequently asked questions

Why do I have to do the same thing to both sides?

An equation is like a balance scale. Adding, subtracting, multiplying or dividing both sides by the same number keeps them equal (just never divide by zero). So the new equation has exactly the same answer as the old one. That's what makes each step safe.

How do I solve an equation with fractions?

Multiply both sides by the least common denominator, the smallest number every bottom part divides into. For (x + 4)/3 = 2x − 1, multiplying by 3 gives x + 4 = 6x − 3. Then gather the terms: 7 = 5x, so x = 7/5. The solver does this for you and shows the step.

What does 'no solution' mean?

The unknown cancels out and leaves a false statement. For 2(x + 3) = 2x + 5, multiplying out gives 2x + 6 = 2x + 5. Subtracting 2x leaves 6 = 5. No value of x can make that true.

What does 'infinitely many solutions' mean?

The unknown cancels out and leaves a true statement such as 6 = 6. The two sides are the same expression written in different ways, so any value of x works. 2(x + 3) = 2x + 6 is an example.

Can it solve x² equations?

Only when the squared terms cancel, as in x² + 2x = x² + 8. A true quadratic such as x² − 4 = 0 needs the quadratic equation calculator. That one handles two answers, and complex answers too.

How this calculator is checked

Method: Standard properties of equality: expand by the distributive property, add or subtract the same term on both sides, multiply by the least common denominator, divide by the nonzero coefficient. Exact rational arithmetic. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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