An equation is a balance
Perform the same valid operation on both sides to preserve equality. Adding or subtracting the same expression is allowed. Multiplying or dividing by a known nonzero constant is also allowed.
Moving a term across the equals sign is shorthand for one of those operations. Writing the actual subtraction is a good way to avoid sign mistakes.
Collect the unknown and the constants
Subtract the variable terms from one side, then subtract constants from the other. The result has the form Ax = B. If A is nonzero, divide by A.
If A = 0 and B ≠ 0, the equation has no solution. If both are zero, every real number satisfies the original linear equation. A disappearing variable is not automatically an error.
Check against the original equation
Substitute your result into both original sides. They should have the same value. Checking only the last rearranged line will not reveal a mistake made earlier.
The linked solver accepts expanded linear terms in x, decimals and one equals sign. Expand parentheses and clear written fractions first; unsupported notation produces an input error.
LET’S WORK IT THROUGH
Solve 5x − 7 = 2x + 11.
- Subtract 2x from both sides: 3x − 7 = 11.
- Add 7 to both sides: 3x = 18.
- Divide by 3: x = 6.
THE ANSWERx = 6. Both original sides evaluate to 23.
YOUR TURN
A small check for understanding.
Solve 4x + 1 = 4x + 9.
Reveal the answer
No solution. Subtracting 4x leaves the false statement 1 = 9.
Now try your own numbers.
The solve for x includes input guidance and the limits of its supported calculations. Use it alongside the method above.
Open Solve for x ↗A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.