Equality must stay balanced
Subtracting b from the left side requires subtracting b from the right side as well. The familiar sign change is the simplified result of applying the same operation to both sides, not a rule about moving symbols.
One-Variable Linear Equation Calculator with Steps
Solve ax + b = c with balancing steps, substitution checks and guidance for signs, coefficients and valid equation models.
Free learning toolValidated inputs and visible working
YOUR RESULT
Your solution for x
Enter your valuesChoose an example or type the known values, then calculate to see the answer and working.
Balance, coefficients and substitution
The coefficient multiplies x
In -2x, the coefficient is -2, including its sign. Dividing both sides by a negative coefficient changes the sign of the quotient. Entering 2 instead solves a different equation.
Substitution closes the loop
Replace x in the original equation, not only in a rearranged line. If the left side evaluates to c, the value satisfies the equation. This check is quick enough to make every solver use accountable.
How a one-variable equation is solved
A linear equation states that two expressions are equal and contains an unknown with power one. This calculator solves equations already arranged as ax + b = c. It shows the subtraction of the constant and division by the coefficient, then substitutes the result as a check. The calculator solves the equation entered; it cannot confirm that a word problem was translated into the correct equation.
Recognise the linear form ax + b = c
Use it after defining x and rewriting the relationship in the supported form. Combine like terms and expand brackets on paper first if needed. The coefficient a must be non-zero; if a is zero, the statement may be always true, impossible or no longer an equation in x. Keep negative signs attached to their coefficients when entering values.
Worked example: Solve 3x - 5 = 16
The coefficient is 3, the constant is -5 and the right side is 16.
Prediction first
Estimate the sign, scale, range or likely form of the answer before calculating. A prediction makes an input error easier to notice.
- Step
Add 5 to both sides: 3x - 5 + 5 = 16 + 5, giving 3x = 21.
- Step
Divide both sides by 3 to isolate x: x = 21 ÷ 3 = 7.
- Step
Substitute 7 into the original left side: 3(7) - 5 = 21 - 5 = 16.
- Step
The check matches the right side, so x = 7 is a solution.
Linear-equation errors that break equality
| Mistake | Why it fails | Better check |
|---|---|---|
| Dropping a negative sign | Changing -5 to 5 changes both the rearrangement and solution. | Enter each coefficient and constant with the sign shown in standard form. |
| Dividing only one term | From 3x = 21, division applies to the entire side, not a selected digit. | Show the division bar across both sides and simplify completely. |
| Skipping the model | A valid algebra answer can be impossible for an age, length or item count. | Define x, retain units and test the final value in the original context. |
Check the solution in a new equation
The result points to related practice, but the best next step depends on what the learner could explain without help.
One-Variable Linear Equation Calculator questions
What if the equation has brackets?
Expand and collect like terms first, then rewrite it as ax + b = c before entering the three coefficients.
Can a, b or c be decimals?
Yes, finite decimal values are accepted. Preserve exact fractions on paper if rounding would weaken a later result.
Why is a = 0 rejected?
With no x term, division by a would mean division by zero. The remaining statement needs a different identity-or-contradiction analysis.