Linear equation calculator
Solve equations of the form ax + b = c and check the answer automatically.
Calculator inputs
Results
Enter your values and press “Calculate” to see the result.
In short
- What it calculates
- Solve equations of the form ax + b = c and check the answer automatically.
- Formula used
ax + b = c- Example
- 2x + 5 = 17
Linear equation calculator
Any first-degree equation can be rearranged into ax + b = c. Enter the three coefficients and you get the exact solution together with the verification step.
How it works
Subtract b from both sides, then divide by a. If a is zero the equation has no unique solution: either no number works, or every number does.
Formula
ax + b = c
x = (c − b) / a
Worked example
2x + 5 = 17
x = (17 − 5) / 2 = 6
Check: 2 × 6 + 5 = 17 ✓
Explanation
Solving means doing the same to both sides
The whole technique reduces to one idea: an equation is a balanced scale, and any operation applied to one side must be applied to the other. Adding, subtracting, multiplying or dividing by the same number preserves the equality. That is the only principle to internalise; the rest is orderliness.
The three possible cases
If solving leaves x equal to a number, there is a unique solution. If it leaves an identity such as 0 equals 0, any value works and the equation has infinitely many solutions. If it leaves something impossible such as 0 equals 5, there is no solution. The last two cases surprise people who always expect a number.
A classic mistake with fractions
Multiplying the whole equation by the common denominator is correct, but you must multiply every term, including those without a fraction. Missing just one changes the result, and it is the most repeated error in exercises.
Checking is quick
Substituting the solution into the original equation and seeing whether it holds takes ten seconds and catches almost any sign error. It is always worth doing.
Frequently asked questions
What if x appears on both sides?
Collect terms first: 3x + 2 = x + 10 becomes 2x + 2 = 10, so a = 2, b = 2 and c = 10.
What does a = 0 mean?
The x term disappears. If b and c match there are infinitely many solutions; otherwise the equation is impossible.
Can an equation have no solution?
Yes. If solving leads to a false equality such as 0 equals 5, there is no solution. If it leads to 0 equals 0, every number satisfies it.
How do I check my answer?
By substituting the value obtained into the original equation. If both sides match, the solution is correct.
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