Interactive linear equation solver showing balance principle and inverse operations

Equations aren't puzzles — they're balances

The secret to solving any linear equation isn't memorising steps — it's understanding that both sides must stay equal, and operations must be reversed in the exact opposite order they were applied. Move the slider to adjust the variable and watch how balance is maintained.

Balance View BALANCED
Adjust x to balance both sides of the equation
x = 0 → Left: 0 | Right: 6
x = -5 x = 0 x = 5 x = 10 x = 15
Current x
0
Balance Status
Off
When solving 2x + 3 = 9, you must eliminate the addition term (+3) before dealing with the multiplication (×2). This isn't arbitrary — it reverses the order operations were originally applied. To isolate x, subtract 3 from both sides first (giving 2x = 6), then divide both sides by 2 (giving x = 3). If you tried to divide by 2 first, you'd get x + 1.5 = 4.5, which is harder to work with and breaks the systematic approach. Always work backwards through operations: undo addition/subtraction first, then multiplication/division.
Know This
Always eliminate addition or subtraction terms first before dealing with multiplication or division, and check your solution by substituting back into the original equation to verify both sides equal.