Math calculator

Linear Equation Calculator

Solve an equation in the form ax + b = c and show the balancing steps. Each submitted value produces solution plus the intermediate reasoning.

Linear Equation inputs

Start with the given values

When the result is useful

Linear equations model fixed fees plus per-unit charges, constant-speed relationships, temperature conversions, and many first-stage algebra problems. A related application of Linear Equation is linear rate of change.

Reading the calculation

A one-variable linear equation asks for the value that keeps both sides equal. Isolating x means applying inverse operations to both sides in the same order. For a connected concept in Linear Equation, see linear sequences.

This definition sets the boundary between linear equation and a neighboring calculation with similar inputs.

A worked example

For 4x + 7 = 31, subtract 7 from both sides to obtain 4x = 24. Dividing both sides by 4 gives x = 6, and substitution checks that 4(6) + 7 equals 31. This Linear Equation example can be compared with quadratic equations.

Before relying on the answer

When a equals zero, the equation no longer has one unique linear solution. Depending on b and c, it may be false for every x or true for every x.

An impossible solution sign or magnitude usually points to field assignment before it points to rounding.

Reproducing the answer

Undo addition or subtraction around the variable term first. Then undo multiplication by the coefficient. Substitute the candidate solution into the original equation rather than only the rearranged line.

Using the result beyond this page

Start the linear equation setup by pairing every source number with coefficient a, constant b and right side c. Convert unlike units before typing, and postpone rounding until the displayed solution is ready to report.

Changing c or b shifts the numerator c − b; changing a rescales that difference. A coefficient close to zero can create a very large solution even when the constants look modest. Use that direction of change to check the displayed solution before copying it elsewhere.

This page isolates one unknown in a first-degree equation. Expressions containing x², x in a denominator, or products of unknowns belong to different equation families. Keep that boundary in mind when interpreting the numerical result.

When copying the result elsewhere, include its label and any squared, linear, angular, or percentage unit implied by the inputs. That record distinguishes a calculated solution from an unlabeled number and makes later checking substantially easier.

For later verification, record coefficient a, constant b and right side c before rounding the solution. The unrounded working value can feed subsequent steps while the rounded value serves presentation.

A few useful clarifications

Why perform the same operation on both sides?

It preserves equality, much like changing both pans of a balanced scale equally.

Can coefficients be decimals?

Yes. Decimal and negative coefficients are valid as long as a is nonzero.

How is the answer checked?

Replace x in ax + b with the result and verify that the expression equals c.

What if a is zero?

There is either no solution or infinitely many solutions, not one isolated x.

Is 2(x + 3) = 10 supported directly?

Expand it to 2x + 6 = 10 before entering a = 2, b = 6, and c = 10.