🔢 Linear Equation Calculator
Solve the linear equation ax + b = 0.
0 = ax + b
What is a Linear Equation?
An equation where the highest degree of the unknown variable is 1.
Solution Formula
ax + b = 0 → x = −b / a
a must not be 0. If a = 0, it is not an equation.
Worked examples
2x − 6 = 0 gives x = 3: add 6 to both sides and divide by 2 to isolate the unknown.
−3x + 12 = 0 gives x = 4; a negative coefficient only flips the sign of the answer, the method is unchanged.
What the solution assumes
The coefficient a must not be 0. With a = 0 the statement collapses to b = 0, which is either always true or never true and has no single solution. A linear equation in one unknown always has exactly one answer, so there is no zero-root or two-root case. Decimal inputs are accepted and rounding only affects the display.
Frequently asked questions
- Why is a = 0 rejected?
- The equation stops being linear: 0 × x + b = 0 leaves nothing to solve for and is either an identity (b = 0) or a contradiction.
- How do I solve it by hand?
- Subtract b from both sides, then divide by a: x = −b / a. For 2x − 6 = 0 that is 6 / 2 = 3.
- What does the solution mean on a graph?
- The graph of y = ax + b is a straight line and the root is where it crosses the x-axis; the slope a sets how steeply the line rises.