🎓 Mathematics • Algebra
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Linear Equation Solver
Dedicated solver for linear equations ax + b = c with step-by-step balance method arithmetic.
Algebra & Matrix Engine
Algebra & Matrix Studio
Solve quadratic equations with complex roots, 2x2 systems via Cramer's rule, binomial FOIL expansions, and 2x2/3x3 matrix linear algebra with instant proofs.
Solver Mode
Standard linear equation form: ax + b = c
Single Variable Linear Equation
3x + 7 = 22
x = 5
Step-by-Step Algebraic Isolation
Original equation: 3x + 7 = 22
Subtract 7 from both sides: 3x = 22 - (7) = 15
Divide both sides by 3: x = 15 / 3
Final solution: x = 5
What is a Linear Equation?
A linear equation contains variables with power 1. When plotted on a coordinate plane, it forms a straight line.
Formula & Step-by-Step Calculation
ax + b = c ⟹ x = (c - b) / a
Subtract b from both sides and divide by coefficient a.
Worked Step-by-Step Examples
Example 1
Solve 5x - 15 = 0
Solution: x = 3
• 5x = 15 ⟹ x = 3
Common Real-World & Academic Use Cases
- ✓ Introductory algebra
- ✓ Balancing budgets
- ✓ Physics rate equations
How to Use the Linear Equation Solver
1
Input a, b, c
Enter equation values.
2
View Steps
Inspect algebraic isolation steps.
Frequently Asked Questions
Q: Can a equal 0?
If a = 0 and b ≠ c, the equation has no solution.