Test linear expressions using coefficients, constants, and side comparisons. Spot impossible equations before solving variables. Review steps, sample rows, exports, and solution status instantly.
Start with the linear equation ax + b = cx + d.
Move variable terms to one side and constants to the other side.
(a - c)x = d - b
If a - c = 0 and d - b ≠ 0, the equation has no solution.
If a - c = 0 and d - b = 0, the equation has infinitely many solutions.
If a - c ≠ 0, then x = (d - b) / (a - c).
Enter the coefficient of x on the left side.
Enter the constant on the left side.
Enter the coefficient of x on the right side.
Enter the constant on the right side.
Click Calculate to classify the equation.
Read the original equation, simplified equation, and status.
Use the export buttons to save the current result.
| Equation | Simplified Form | Status |
|---|---|---|
| 2x + 5 = 2x + 1 | 0x = -4 | No solution |
| 3x + 4 = 3x + 4 | 0x = 0 | Infinitely many solutions |
| 5x - 2 = 2x + 7 | 3x = 9 | One solution |
| -x + 6 = -x + 9 | 0x = 3 | No solution |
| 4x + 8 = x + 17 | 3x = 9 | One solution |
A which equation has no solution calculator checks whether a linear equation creates a contradiction. It compares both sides after simplification. This helps students test equations quickly. It also reduces algebra mistakes.
The tool studies equations in this form: ax + b = cx + d. It brings variable terms together. It also groups constant terms. Then it decides the equation type. The result can be one solution, no solution, or infinitely many solutions.
A linear equation has no solution when the x terms cancel, but the constants disagree. This creates an impossible statement. A common example is 2x + 5 = 2x + 1. Subtract 2x from both sides. You get 5 = 1. That statement is never true.
This calculator highlights that contradiction immediately. It shows the simplified form. It also explains why no x value works. That makes it useful for homework, class practice, and self study.
Many learners confuse no solution with infinite solutions. This page separates them clearly. If coefficients match and constants differ, the equation has no solution. If coefficients and constants both match, the equation has infinitely many solutions. Otherwise, the equation has one solution.
The calculator also supports quick exports. You can save your result as CSV. You can also print the result as a PDF. The example data table helps you compare patterns across multiple equations.
Use this calculator for algebra lessons, worksheets, tutoring sessions, and revision. It is useful when checking equations, verifying class examples, or understanding contradiction statements. It also supports better pattern recognition. Once you see how matching coefficients behave, equation classification becomes much easier.
After you enter values and submit, the result appears above the form. You will see the original equation, the simplified equation, and the final classification. When a contradiction appears, the page states that no solution exists. This step by step structure improves understanding and makes review faster.
It also helps teachers explain why some equations fail for every value.
No solution means no value of x can make the equation true. After simplification, the statement becomes impossible, such as 4 = 9.
Check whether the x coefficients become equal while the constants stay different. That pattern creates a contradiction and proves there is no valid solution.
Yes. If the variable terms do not cancel completely, the calculator computes the single value of x and displays it clearly.
Yes. If both sides simplify to the same expression, every real value satisfies the equation, so the result is infinitely many solutions.
It uses the linear form ax + b = cx + d. You enter the four numbers, and the page classifies the equation.
Yes. The inputs accept decimals, so you can test simple fractions, measured values, and non integer algebra examples.
The simplified equation shows the pattern directly. It helps you see whether the variable disappears, whether a contradiction appears, or whether one value remains.
For ax + b = cx + d, no solution happens when a equals c and b does not equal d. The variable cancels, but the constants disagree.