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Linear Equation Solver

Solve equations of the form ax + b = c.

Equation Inputs

Enter the coefficients for ax + b = c.

Solution
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Calculation Breakdown:

Enter values to solve.

About this topic

Standard Linear Equation (ax + b = c) Isolate the variable x in a straight-line equation.

A linear equation contains a variable whose highest power is 1. Solving it means performing the same operation on both sides until the variable is isolated. For example, in 2x + 5 = 15, subtract 5 from both sides to get 2x = 10, then divide by 2 to find x = 5. Linear equations are used to find unknown quantities in situations involving fixed rates, costs, distances, and simple budgets.

Key formulas & rules

  • •Formula: x = (c - b) / a
  • •Requires a ≠ 0
  • •Straight-line solution
  • •Unique solution if a ≠ 0
  • •Handles fractions and decimals

Examples

Input Output Note
2x + 5 = 15 x = 5 Standard
3x - 6 = 9 x = 5 Negative constant
0.5x + 2 = 4 x = 4 Decimal coefficient
10x = 100 x = 10 No constant term

Real-world uses

Budgeting Physics kinematics Linear programming
Special Cases (Zero & Infinite Solutions) Understand edge cases where a = 0.

When the coefficient of the variable is zero, the variable disappears and the equation becomes a statement about constants. If both sides are equal, such as 0x + 5 = 5, every value of x satisfies the equation, so there are infinitely many solutions. If the constants are different, such as 0x + 5 = 10, no value of x can make the statement true, so there is no solution. Recognising these cases helps distinguish identities from contradictions.

Key formulas & rules

  • •If a = 0 and b = c → Infinite Solutions
  • •If a = 0 and b ≠ c → No Solution
  • •Occurs when variable cancels out
  • •Identity = always true
  • •Contradiction = never true

Examples

Input Output Note
0x + 5 = 5 Infinite Identity
0x + 5 = 10 None Contradiction
0x = 0 Infinite Any x works
0x = 5 None Impossible

Real-world uses

Error checking Logic puzzles System contradictions

Modes & formulas

1

Solve for x

• Isolates the variable x on one side of the equation. • Enter the coefficients a, b, and c. • The calculator subtracts b from c, then divides by a.
x = (c - b) / a

If 'a' is 0, the equation is no longer linear (it's a constant). The tool handles edge cases where there are infinite solutions (0=0) or no solutions (0=5).

How to use it

Enter the values for a, b, and c. The tool solves for x and displays the exact decimal or fraction.

Frequently asked questions

What if 'a' is zero?
If a=0, there is no variable to solve for. The equation becomes b=c, which is either always true (infinite solutions) or always false (no solution).
Why is it called 'linear'?
Because when graphed, all solutions (x, c) satisfying the equation lie on a straight line.
What is a linear equation?
An equation where the highest power of the variable is 1. When graphed, it forms a straight line.
What is the standard form ax + b = c?
It is a common way to write a linear equation, where a is the coefficient, b is a constant, and c is the result.
What does "Infinite solutions" mean?
It means any number you plug in for x will make the equation true. This happens when both sides of the equation are identical (e.g., 5 = 5).
What does "No solution" mean?
It means there is no number that can make the equation true. This happens when you get a false statement like 5 = 10.

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Percentage Calculate percentages, increases, and decreases. Fraction Add, subtract, multiply, and divide fractions. Ratio Solve proportions and simplify ratios. Average Find mean, median, and average of a dataset. Exponent & Root Calculate powers and bases. Square Root & N-th Root Find square roots and radical values.
Read the full Linear Equation guide — examples & 18 FAQs