How do I solve ax + b = 0?
Move b to the other side and divide by a: x = −b / a. For 2x − 6 = 0, x = 6 / 2 = 3.
// maths › Algebra
Linear equation solver
Solve ax + b = 0 for x, and see where the line crosses zero.
ax + b = 0 → x = −b / a
Frequently asked questions
What does the root mean on the graph?
The root is the x-value where the line crosses the horizontal axis — the single point where y equals zero.
What does the slope tell me?
The slope a is how steep the line is: how far y changes for each step in x. A bigger a makes a steeper line; a negative a tilts it downward.
Where is this used in real life?
Break-even points — if profit is 5x − 200, solving 5x − 200 = 0 shows you must sell 40 units to break even. Converting units — a linear rule links Celsius and Fahrenheit. Phone plans — a $20 base plus $0.10 a minute is a straight-line cost, and solving for a target bill tells you how many minutes you can use.
When does a linear equation have no solution?
When a = 0 but b is not zero, the equation becomes b = 0, which is false, so there is no x that works. If a = 0 and b = 0, every x works.