Solve Linear Equations (ax + b = c) with Step-by-Step Solutions
2x + 5 = 15
x
+
=
Result
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📝 Step-by-step solution
Enter coefficients and click "Solve Equation"
💡 Equation form: a·x + b = c | Solve for x | a ≠ 0
📖 What is a Linear Equation?
A linear equation is an equation where the highest power of the variable is 1.
The standard one-variable form is a·x + b = c, where a, b,
and c are constants and x is the unknown variable.
Solving for x means isolating it on one side of the equation.
This calculator solves equations of the form a·x + b = c and provides
step-by-step solutions — perfect for students learning basic algebra.
🧮 Formula
Equation: a·x + b = c Solution: x = (c − b) ÷ a Condition: a ≠ 0
📝 Worked Example
Example 1: Solve 2x + 5 = 15
Step 1: Write the equation: 2x + 5 = 15 Step 2: Subtract b from both sides: 2x = 15 − 5 = 10 Step 3: Divide both sides by a: x = 10 ÷ 2 Result:x = 5
Example 2: Solve 3x − 7 = 8
Step 1: Write the equation: 3x − 7 = 8 Step 2: Add 7 to both sides: 3x = 8 + 7 = 15 Step 3: Divide both sides by 3: x = 15 ÷ 3 Result:x = 5
💡 Rules for Solving Linear Equations
Addition/Subtraction Rule: You can add or subtract the same number from both sides.
Multiplication/Division Rule: You can multiply or divide both sides by the same non-zero number.
Isolate the variable: Get all terms with x on one side, constants on the other.
Check your answer: Substitute x back into the original equation to verify.
📊 Common Use Cases
Age problems: "In 5 years, John will be 3 times as old as..."
Money problems: "If you buy 3 items and pay ₹15 with ₹5 discount..."
Distance problems: "A car travels at 60 km/h and covers..."
Geometry: Finding unknown side lengths given perimeter or area.
Physics: Rearranging formulas (e.g., v = u + at).
⚠️ Limitations & Assumptions
📌 Important Notes
Only solves linear equations of the form a·x + b = c.
Requires a ≠ 0. If a = 0 and b = c, there are infinite solutions. If a = 0 and b ≠ c, there is no solution.
Does not solve quadratic, polynomial, or system-of-equations problems.
Results are shown in decimal form, not as fractions.
Values may be decimals or negative — calculator handles both.
📚 Sources & References
Authoritative Sources
OpenStax — Elementary Algebra
Khan Academy — Linear Equations in One Variable
Math is Fun — Linear Equations
Larson, R. — Elementary Algebra
❓ Frequently Asked Questions
What is a linear equation?
A linear equation is an equation where the variable (usually x) has an exponent of 1.
Its graph is a straight line. The standard form is a·x + b = c.
What if a = 0?
If a = 0, the equation becomes b = c.
• If b = c → infinite solutions (any value of x works)
• If b ≠ c → no solution (the equation is contradictory)
Can the solution be a decimal?
Yes! For example, 3x = 10 gives x = 10/3 ≈ 3.3333. This calculator displays such results to 6 decimal places.
Can I solve equations with x on both sides?
Yes, but you first need to move all x-terms to one side and constants to the other. For example,
2x + 5 = x + 10 becomes x = 5. Then enter a = 1, b = 0, c = 5.
How do I verify the answer?
Substitute the value of x back into the original equation.
If both sides are equal, the answer is correct.
This Algebra Calculator is provided for informational and educational purposes only.
It solves basic linear equations of the form a·x + b = c. For more complex algebra,
please consult a textbook or a qualified math teacher. Online Calculator Zone is not
responsible for any decisions or results based on this tool.