vmbo havo vwo
Linear equation solver
Quick answer
For ax + b = c, use x = (c − b) / a. Example: 2x + 3 = 11 gives x = 8 / 2 = 4.
If x also appears on the right, move the x terms to one side. If a = 0, x disappears and there is no unique solution.
Calculator
Choose one side or two sides. Use ± when you need a minus sign. On iOS the decimal keypad has no minus key: use ± next to the field.
What is a linear equation?
Linear means x appears to the first power only — not as x². The graph is a straight line. You solve with the balance method: whatever you do on the left, do on the right, as if you were keeping a scale level.
| Form | Example | First step |
|---|---|---|
| ax + b = c | 2x + 3 = 11 | Move the constant, then divide by a |
| ax + b = cx + d | 5x + 2 = 2x + 11 | x terms to one side, constants to the other |
On vmbo (the more practical Dutch track) this starts with sums like 2x + 3 = 11. On havo and vwo (middle and university-preparatory tracks) you meet x on both sides, or brackets you clear first. If the problem has x², open the quadratic formula calculator.
Examples by level
2x + 3 = 11
- Move 32x = 11 − 3 = 8
- Dividex = 8 ÷ 2 = 4
Check: 2·4 + 3 = 11. You undid the constant first, then divided.
5x + 2 = 2x + 11
- x to the left5x − 2x = 11 − 2
- 3x = 9x = 3
Check: left 5·3 + 2 = 17, right 2·3 + 11 = 17.
2x + 3 = 2x + 5. What happens?
- Cancel x3 = 5
- ConclusionThat is false: no solution.
If it were 2x + 3 = 2x + 3, there would be infinitely many solutions: every x works.
Common mistakes
Wrong
From 2x + 3 = 11, writing x = 11 − 3 − 2.
Right
First undo +3 (2x = 8), then divide by 2. Do not subtract everything from x at once.
Wrong
For 5x + 2 = 2x + 11, move only 2x and forget the constants.
Right
Both sides of the balance: x terms and constants. 5x − 2x = 11 − 2.
Wrong
Ignore a = 0 and still divide by a.
Right
You cannot divide by 0. When the x terms cancel, check whether what remains is true or false.
Practice
vmbo 3x + 1 = 10. What is x?
x = 3
3x = 9, x = 3.
havo 4x − 1 = x + 8.
x = 3
4x − x = 8 + 1 → 3x = 9.
vwo 2x + 3 = 2x + 5. How many solutions?
None
x cancels → 3 = 5, which is false.
vwo If the equation has an x², which tool do you use?
The quadratic formula calculator, not this page.
In class
Linear equations appear in every Dutch track. Two equations at once: systems of equations — typically havo/vwo. Quadratic: quadratic formula calculator.
Next step
- How does this work? The explanation and examples are further up this page.
- See it visually Linear function simulation: change the values and watch what happens.
- Test yourself Linear equation practice, with an explanation after every answer.
- Video explanations On the Linear function page. YouTube only loads when you press play.
Learning path
- Next: Systems of equations Two linear equations in two unknowns.
- Related: Quadratic formula calculator
Frequently asked questions
How do you solve ax + b = c?
Use x = (c − b) / a. For 2x + 3 = 11 you get x = 4.
How do you isolate x?
Balance: same operation left and right. Undo constants first, then divide by the coefficient of x.
What if the x terms cancel?
No unique x. A true leftover statement → infinitely many solutions; a false one → no solution.
What if a = 0?
No unique x. Either the statement is never true, or it is always true.