The formula this page uses
ax + b = c → x = (c − b) / a
Algebra Calculator
Solve algebra problems with clear steps, notation, and a final check. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
Result—Choose a mode, enter the known values, and calculate.
Show your work Step-by-step method
- The calculation method and verification will appear here.
Algebra
Algebra Calculator explained
The short version
- Algebra puts a letter where a number is missing, then finds the one value that letter is allowed to be.
- Whatever you do to one side of the equals sign, do to the other side as well. That is the only rule that keeps an equation true.
- A linear equation has one answer, no answer, or every answer, and the last two show up as 10 = 7 or 0 = 0 at the end of your working.
What each part means
SymbolWhat it means
x — The unknownThe number you are solving for. It has no unit of its own until the word problem gives it one.
a — CoefficientThe number multiplying x. If a = 0 the equation is not linear in x any more.
b — Constant on the leftThe number added on the same side as x. Subtract it first.
c — Value on the rightWhat the whole left side has to equal.
Show your work: a full example
- Start with the equation4(x − 3) + 2x = 3x + 15
- Multiply the 4 into both terms4x − 12 + 2x = 3x + 15
- Collect the x terms on the left6x − 12 = 3x + 15
- Subtract 3x from both sides3x − 12 = 15
- Add 12 to both sides3x = 27
- Divide both sides by 3x = 9
- Check by putting 9 back in4(9 − 3) + 2(9) = 24 + 18 = 42 and 3(9) + 15 = 27 + 15 = 42
A second, different case
- A different case: the x terms cancel2(x + 5) = 2x + 7
- Multiply out the left side2x + 10 = 2x + 7
- Subtract 2x from both sides10 = 7
- Read what is left10 = 7 is false for every x, so this equation has no solution
- Change the 7 to a 10 and repeat2x + 10 = 2x + 10 → 10 = 10
- Read that instead10 = 10 is true for every x, so now every number is a solution
Copy-ready example
4(x − 3) + 2x = 3x + 15
Start with the equation
Questions about the Algebra Calculator
Why does 3x mean multiply, but 3½ means add?
Two letters or a number next to a letter always means multiply, so 3x is 3 times x. A mixed number like 3½ is an old piece of arithmetic notation that means 3 + ½. This is exactly why algebra writes 7/2 instead of 3½: it removes the clash.
What is the difference between an expression and an equation?
4x − 12 is an expression: you can simplify it or plug a number into it, but there is nothing to solve. 4x − 12 = 15 is an equation, because it claims two things are equal, and only certain x values make that claim true.
When does an algebra equation have no solution?
When the variable disappears and leaves a false number statement, like 10 = 7. That happens whenever the two sides describe parallel lines: same slope, different intercept, so they never meet.
Do I have to move x to the left-hand side?
No. 9 = x says exactly the same thing as x = 9. Moving x to whichever side keeps its coefficient positive just saves you from dividing by a negative later, which is where sign errors come from.
Calculate, interpret, verify.
This workspace keeps the formula and the meaning together. Decimal results are rounded for display; retain full precision when you continue a calculation.
Enter known values
Match each input to the quantities in the problem and keep units consistent.
Use the relationship
The result panel identifies the formula or algorithm and shows the main substitutions.
Read the visual
Use the diagram, plot, or data display to check scale, direction, and plausibility.
Practice unaided
Move to targeted questions once you can explain why the method applies.
Learn the mathematics
Understand algebra behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.