Using the Linear Equation Calculator
Use this when unknown quantities appear once to the first power. Enter the coefficients of ax + b = cx + d; a negative constant needs its minus sign. This tool accepts whole-number coefficients, rather than arbitrary typed expressions.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- a · x (left)
- 3
- b (left constant)
- 5
- c · x (right)
- 1
- d (right constant)
- 13
Example result
- Solution
- x = 4
- Decimal approximation
- 4
- Verification
- Left side = right side = 17
- Steps
- Start with 3x + (5) = 1x + (13). Subtract 1x and 5 from both sides: 2x = 8. Divide both sides by 2: x = 4. Substitute into the original equation; left and right sides agree (rounding may affect the decimal display).
Method and assumptions
Collect x terms on one side and constants on the other, then divide. Integer coefficients from −10,000 to 10,000; exact fraction results. Identical and contradictory equations are handled separately.
Reference: openstax.org — method and further reading
Check the answer in the original problem
After solving, substitute the result into the original equation or relationship where possible. This can catch a sign error or a coefficient entered in the wrong position. Keep the exact inputs available when comparing with another tool, since changing a coefficient or rounding an intermediate value can change the problem being solved.
Common question
Why does my equation have no single answer?
When both sides simplify to the same expression, every real x works. If they simplify to different constants, no value of x can make the equation true.