Linear Equation
Solve ax + b = c
Solve: ax + b = c
About This Calculator
A linear equation in one variable is an equation of the form ax + b = c, where the unknown x appears only to the first power. Solving it means isolating x by performing the same operations to both sides. Linear equations model constant-rate relationships and appear in virtually every applied field.
Formula
ax + b = c
x = (c − b) / a
For two unknowns: ax + by = c and dx + ey = f → solve by substitution or elimination
Example Calculation
Solve 3x + 7 = 22.
- Subtract 7 from both sides: 3x = 15
- Divide both sides by 3: x = 5
- Check: 3(5) + 7 = 22 ✓
x = 5
Solving Linear Equations — Examples
| Equation | Step 1 | Step 2 | Answer |
|---|---|---|---|
| 2x + 3 = 11 | 2x = 8 | x = 4 | x = 4 |
| 5x − 10 = 0 | 5x = 10 | x = 2 | x = 2 |
| −x + 6 = 2 | −x = −4 | x = 4 | x = 4 |
| x/3 + 1 = 5 | x/3 = 4 | x = 12 | x = 12 |
| 4x + 2 = 2x + 10 | 2x = 8 | x = 4 | x = 4 |
Frequently Asked Questions
What does it mean to solve a linear equation?
To solve means to find the value(s) of the unknown variable that make the equation true. For a linear equation in one variable there is always exactly one solution (unless coefficients are both zero).
What if x appears on both sides?
Collect all x terms on one side by adding or subtracting. For example, 4x+2=2x+10 → 4x−2x=10−2 → 2x=8 → x=4.
What is the difference between an equation and an expression?
An expression (like 3x+7) has no equals sign and cannot be solved. An equation (like 3x+7=22) asserts equality and can be solved for the unknown variable.
What are simultaneous linear equations?
When two or more linear equations share unknowns, they form a system that can be solved together. Methods include substitution (express one variable in terms of the other) and elimination (add/subtract equations to cancel a variable).