Linear Equation Solver

Solve a linear equation such as 3x + 7 = x − 5 or 2(x − 3) + 4 = 5x/2, with exact fractions and every step shown.

Equation	3x + 7 = x − 5

Equation

Any letter for the unknown. Brackets, fractions and decimals are fine.

3x + 7 = x − 5

x = −6

x = −6. Substituting it back makes both sides equal.

Exact. Checked exactly.

Method: Balance method: do the same to both sides
Worked out with: AllCalcHub exact algebra (fractions, no rounding)
Check: Every step recomputed with exact fractions

The solution on a number line

Each side as a line: they meet at the answer

x = −6at (-6, -11)Point at the chart, or Tab to it and use ← →

Left sideRight sidex = −6: (-6, -11)

1
Subtract x from both sides
2x + 7 = −5
2
Subtract 7 from both sides
2x = −12
3
Divide both sides by 2
x = −6

About the Linear Equation Solver

A linear equation has the unknown only to the first power. The balance method solves it: whatever you do to one side, do to the other. Expand any brackets, gather the unknown on one side and the numbers on the other, then divide.

Every step is checked before it's shown: the calculator proves each new line has exactly the same solution as the one before.

The formula

$ax + b = cx + d \;\Rightarrow\; x = \frac{d - b}{a - c}$

Worked example

3x + 7 = x − 5

Subtract x from both sides: 2x + 7 = −5
Subtract 7 from both sides: 2x = −12
Divide both sides by 2: x = −6

Questions people ask

Can I use a letter other than x?

Yes. Use any one letter, like y or t.

Can it solve x² equations?

Not this one. Use the Quadratic Equation Solver.