How a linear equation is solved
Undo the operations in reverse order. Subtract the constant from both sides, then divide by the number in front of x.
3x + 5 = 17 becomes 3x = 12, then x = 4. Both sides then read 17, which is the check.
Worked example
Solve 3x + 5 = 17. Subtract 5 from both sides to get 3x = 12, then divide by 3 to get x = 4.
Substituting back: 3 × 4 + 5 = 17, so the answer is right.
When x appears on both sides
Choose the both-sides form and the same two moves still work: collect the x terms on one side and the numbers on the other.
For 3x + 5 = x + 9, subtracting x gives 2x + 5 = 9, then 2x = 4, so x = 2.
Equations with no single answer
If the x terms cancel and the numbers match, every value of x works. If they cancel and the numbers differ, no value works.
The calculator says which of those happened rather than returning a number that does not exist.
Inputs for the linear equation calculator
What does the equation look like?
Pick the one-sided form ax + b = c, or the both-sides form ax + b = cx + d.
Coefficient of x
The number multiplying x. It cannot be zero, because then there is no x term to solve for.
Constants
The numbers standing on their own. They can be negative.
CALCULATOR QUESTIONS
Linear equation calculator with solution questions
How do I solve 3x + 5 = 17?
Subtract 5 from both sides to get 3x = 12, then divide by 3. The answer is x = 4.
What if x appears on both sides?
Subtract the smaller x term from both sides first, then solve what is left. 3x + 5 = x + 9 gives 2x = 4, so x = 2.
Why does the coefficient of x matter?
The final step divides by it. A coefficient of zero would mean dividing by zero, so the equation is not linear in x at all.
How can I check my answer?
Put the value back into the original equation. Both sides should come out the same, which is what the check rows show.