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 undone in the reverse of the order they were applied to x. Step through the moves: the same move on both sides keeps the scale level; a move on one side only tips it.
Balance viewLevel
Step through: the same move on both sides keeps the scale level
Start: 2x + 3 = 9
Start− 3÷ 2
Equation now
2x + 3 = 9
Left · right at x = 3
9 · 9
To solve 2x + 3 = 9, undo what was done to x in the reverse order. x was doubled, then 3 was added, so take 3 from both sides first (2x = 6), then halve both sides (x = 3). The order comes from the equation, not a fixed rule: in (x + 3) ÷ 2 = 9 the last thing done was dividing by 2, so multiply both sides by 2 first (x + 3 = 18), then take 3 (x = 15). In 2(x + 3) = 10, dividing both sides by 2 first is simplest (x + 3 = 5, so x = 2).
Know This
Undo the operations in the reverse of the order they were applied to x (for ax + b = c that means subtract, then divide), doing the same to both sides, and check your solution by substituting back into the original equation to verify both sides equal.