Linear Equation Calculator
Linear Equation Calculation Method
Equation
Formula for the solution
x = 3
About This Calculator
A linear equation contains the unknown x only once, once everything is rearranged into the form ax + b = 0. Dividing both sides by a gives the solution x = −b/a, which requires a to be non-zero.
If the equation is not already in that form — for example 3x + 5 = 7 — move every constant to one side to get 3x − 2 = 0, then solve. The answer is x = 2/3.
A break-even question is a linear equation in disguise. With fixed costs of 800, variable costs of 4 per unit and a price of 9 per unit, profit starts at 9x = 800 + 4x, which rearranges to 5x − 800 = 0 and gives x = 160 units. That single rearrangement is exactly what this calculator performs.
Key Formula:
ax + b = 0 ⇒ x = −b / a (a ≠ 0)Frequently Asked Questions
What happens when a is 0?
With a = 0 the x term disappears and the equation is no longer linear. If b is also non-zero there is no solution; if b is zero as well, every x is a solution. The calculator shows a notice in both cases.
How is a fractional solution displayed?
The calculator shows a decimal, so a repeating value is rounded: 3x − 2 = 0 gives 0.666667 while the exact answer is 2/3. Use the fraction calculator when you need the exact fraction.
How do I check a linear solution?
Substitute it back into the original equation. For 2x − 6 = 0 the solution x = 3 gives 2 × 3 − 6 = 0, so it is correct. If the two sides do not match, an arithmetic slip happened while rearranging, usually with a sign.
How do I solve 3(x − 2) = 5x + 4?
Expand the bracket first: 3x − 6 = 5x + 4. Move everything to one side to get −2x − 10 = 0, so x = −5. Enter a = −2 and b = −10 in the calculator to confirm the same result.