Quadratic Equation Solver (ax² + bx + c = 0)
About Linear Equation Solver
The Step-by-Step Single-Variable Linear Equation Solver solves algebraic equations ($ax + b = cx + d$), inequalities ($<, \le, >, \ge$), and absolute value equations with full step-by-step simplification, variable isolation, and fraction arithmetic.
How to Use Linear Equation Solver
Step 1
Type your linear equation into the input box (e.g. `5x - 3 = 2(x + 6)`).
Step 2
Click "Solve Linear Equation".
Step 3
Review computed variable value and step-by-step algebraic proof.
Step 4
Click "Copy Solution".
Practical Use Cases for Linear Equation Solver
Algebra Homework Verification & Step-by-Step Learning
Verify homework equations with complete step-by-step algebraic explanations (expanding parentheses, combining like terms, isolating variables).
Break-Even Business Revenue & Cost Equality Modeling
Solve for unit sales volume where total revenue equals fixed and variable operating costs ($P \times Q = F + V \times Q$).
Input & Output Examples
Solving Linear Equation with Parentheses and Fractions
Equation: `3(2x - 4) + 5 = 2x + 9`
Solution: `x = 4.0` | Step 1: Expand: `6x - 12 + 5 = 2x + 9` | Step 2: Combine: `6x - 7 = 2x + 9` | Step 3: Isolate: `4x = 16` → `x = 4`
Key Features & Performance
- ✓Solves: Standard Linear Equations ($ax + b = c$), Multi-Step Equations with Parentheses, Linear Inequalities, Absolute Value Linear Equations.
- ✓Complete Step-by-Step Proof generator explaining every algebraic operation.
- ✓Identifies Infinite Solutions (Identities) and No Solution (Contradictions) cases.
- ✓100% Client-Side math engine.
- ✓1-Click Copy solution & step breakdown.
Key Terminology & Definitions
Linear Equation
An algebraic equation in which each term has an exponent of 1, graphing as a straight line on a coordinate plane.
Identity (Infinite Solutions)
An equation that is true for all real values of $x$ (e.g. $2x + 4 = 2(x + 2) \rightarrow 0 = 0$).