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Linear Equation Solver

Solve ax + b = 0 for x

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📚 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.