Standard Form
\(ax + b = c\)
Linear Equation Solver
Solve linear equations with step-by-step solutions
Explore the line ax + b = c
Drag the a, b, c sliders. The blue line is y = ax + b; the orange horizontal line is y = c. The intersection is the solution.
Quick presets
2.00
-5.005.00
3.00
-10.0010.00
7.00
-10.0020.00
Predict what will happen
What happens to the solution if you double the slope a but keep b and c the same?
Try a = 2 versus a = 4 with b = 0 and c = 8.
Notice
When you change a or b, the blue line tilts or shifts. The solution is wherever it crosses the orange y = c line.
Common mistake
Don't forget to subtract b before dividing by a. The right side is (c − b) / a, not c / a − b.
Why it works
Solving ax + b = c is geometric: find the x where the line y = ax + b reaches the height y = c.
Results
Final Answer
The solution is \(x = 2.0000\)
Step-by-step Solution
- Given: \(2.00x + 3.00 = 7.00\)
- Subtract b from both sides: \(2.00x = 7.00 - (3.00) = 4.00\)
- Divide both sides by a: \(x = \frac{4.00}{2.00} = 2.0000\)
The solution x is the point where the line y = 2.00x + 3.00 reaches the height y = 7.00.
Linear Equations
Linear equations in one variable can be solved using inverse operations.
Key Points:
- Linear equations have exactly one solution
- The coefficient of x (a) cannot be zero
- Always check your solution by substituting back
- Use inverse operations to isolate the variable
Solve for x in the form ax + b = c
\(ax + b = c\)
Worked Examples
Solution Formula
\(x = \frac{c - b}{a}\)
Example: 2x + 3 = 7
\(2x = 4 \Rightarrow x = 2\)
Example: -3x + 5 = 14
\(-3x = 9 \Rightarrow x = -3\)