📏
Linear Equation Solver
Solve ax + b = 0 for x
Share Linear Equation
📚 Examples, Rules & Help
⚡Quick Examples of Linear Equations
📐Linear Equations Formula
General Form:
ax+b=0
Solution:
x=
-b
a
Where a and b are constants and a ≠ 0
🔍How to Calculate Linear Equations
Isolation Method
To solve, isolate the variable by moving the constant term to the right side, then divide by the coefficient
Step-by-Step Process
1. Start with ax + b = 0
2. Subtract b from both sides: ax = -b
3. Divide both sides by a: x = -b/a
🌍Real-World Applications
💰 Finance
Break-even analysis, simple interest calculations
⚡ Physics
Motion at constant velocity, electrical circuits
📊 Business
Cost analysis, linear pricing models
🏠 Real Estate
Linear depreciation, rent calculations
❓Frequently Asked Questions
What if coefficient 'a' is zero?
If a = 0, the equation becomes 'b = 0'. If b is also 0, every number is a solution. If b ≠ 0, there's no solution.
Can linear equations have fractions?
Yes! Linear equations can have fractional coefficients. The solving process remains the same: isolate the variable.
How do I check my answer?
Substitute your solution back into the original equation. If both sides are equal, your answer is correct.
What's the difference between ax + b = 0 and ax + b = c?
Both are linear equations. For ax + b = c, subtract c from both sides to get ax + (b-c) = 0, then solve normally.
💡Calculator Tips & Best Practices
💡Always Isolate the Variable
Move all terms with the variable to one side and constants to the other
⚠️Coefficient Cannot Be Zero
For a linear equation ax + b = 0, coefficient 'a' must be non-zero
⭐Check Your Work
Always substitute your answer back into the original equation to verify
💡Work with Fractions
If coefficients are fractions, consider multiplying the entire equation by the LCD
📚 References & Further Reading
Comprehensive coverage of linear equations and algebraic problem solving
External Link
Interactive lessons on solving linear equations
External Link
Note: These references provide additional mathematical context and verification of the formulas used in this calculator.