About

In real-world applications-such as engineering tolerances, financial interest calculations, or chemistry stoichiometry-coefficients are rarely perfect integers. This tool solves linear equations of the form ax + b = cx + d where values are decimals.

Unlike simple integer solvers, this calculator maintains floating-point precision through the intermediate steps of grouping like terms and isolating the variable. It handles scenarios involving infinite solutions or no solution contradictions cleanly.

Formulas

The goal is to transform the equation into the form x = k.

ax + b = cx + d

Subtract cx from both sides:

(a − c)x + b = d

Subtract b from both sides and divide:

x = d − ba − c

Reference Data

Equation Type	Example	Step 1: Group x	Step 2: Group Constants	Result
Simple Decimal	0.5x = 10	-	-	x = 20
Two-Step	0.2x + 1.4 = 4	0.2x = 2.6	-	x = 13
Variables Both Sides	2.5x − 1 = 1.5x + 3	1.0x − 1 = 3	1.0x = 4	x = 4
High Precision	0.003x = 0.09	-	-	x = 30
Identity	1.2x = 1.2x	0 = 0	-	Infinite Solutions
Contradiction	x = x + 5.5	0 = 5.5	-	No Solution
Negative Coeff	-0.5x = 2	-	-	x = -4
Complex	1.1x + 0.2 = 2.4	1.1x = 2.2	-	x = 2

Frequently Asked Questions

Currently, this tool solves equations already expanded into the form ax + b = cx + d. You should distribute any parentheses manually before entering the coefficients.

The result is calculated to standard floating-point precision. If the result is a non-terminating decimal, it will act according to standard JavaScript precision (approx. 15-17 digits).

If x is eliminated (e.g., 2x = 2x + 1), the tool checks the remaining constants. If 0 = 1, it reports "No Solution". If 0 = 0, it reports "Infinite Solutions".

Yes, integers are treated as decimals (e.g., 5 is 5.0) and will work perfectly.