Solve Linear Equations Instantly
A linear equation is an equation where the variable is only raised to the first power, so its graph is a straight line. This linear equation solver handles equations written as ax + b = c. Enter the coefficient a, the constant b and the constant c, and it solves for x right away. It also correctly identifies the special cases where there is no solution or where every value of x works.
How to Solve ax + b = c
Step 1: subtract b from both sides to get ax = c − b. Step 2: divide both sides by a to get x = (c − b) ÷ a.
Example: 3x + 7 = 22. Subtract 7 to get 3x = 15, then divide by 3 to get x = 5. Check: 3 × 5 + 7 = 22. ✓
Special Cases
- If a = 0 and b = c, the equation is always true, so there are infinitely many solutions.
- If a = 0 and b ≠ c, the equation is never true, so there is no solution.
- If a ≠ 0, there is exactly one solution: x = (c − b) ÷ a.
Frequently Asked Questions
How do I enter an equation like 5 − 2x = 11?
Rewrite it in the form ax + b = c: −2x + 5 = 11. Then enter a = −2, b = 5 and c = 11. The solver gives x = −3.
What if my equation has x on both sides?
Move all the x terms to one side first. For 4x + 2 = x + 14, subtract x from both sides to get 3x + 2 = 14, then enter a = 3, b = 2, c = 14 to get x = 4.
Can this solve equations with decimals or fractions?
Yes. Enter decimal values for a, b and c. For fractions, convert them to decimals first (for example, 1/4 = 0.25).