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Solve a linear equation in the form a x + b = c. Use a negative value for b when the equation contains subtraction.
Show the steps
1. Start with the equation
2x + 3 = 11
2. Move the constant term
Subtract 3 from both sides: 2x = 11 - 3 = 8.
3. Divide by the coefficient of x
x = 8 / 2 = 4.
Method and variables
Linear Equation Calculator
Formula: ax + b = c; x = (c - b) / a
Assumption: The equation has one variable, x, and can be written in the form ax + b = c.
Worked example
Linear Equation Calculator
For 2x + 3 = 11, subtract 3 to get 2x = 8, then divide by 2: x = 4.
Setting up a linear equation from a word problem
A phone plan costs a $12 base fee plus $0.05 per minute. How many minutes fit into a $20 budget? Let x be the minutes: 0.05x + 12 = 20. Subtract 12 to get 0.05x = 8, then divide by 0.05: x = 160 minutes. Check by substituting: 0.05 × 160 + 12 = 20.
| Equation | Step 1: subtract b | Step 2: divide by a | x |
|---|---|---|---|
| 2x + 3 = 11 | 2x = 8 | 8 / 2 | 4 |
| 5x − 7 = 18 | 5x = 25 | 25 / 5 | 5 |
| −3x + 4 = 19 | −3x = 15 | 15 / −3 | −5 |
| 0.05x + 12 = 20 | 0.05x = 8 | 8 / 0.05 | 160 |
If a equals zero there is no unique solution: 0x + 3 = 3 holds for every x, while 0x + 3 = 5 has none.