# Keep the scale balanced Think of a old market scale. If both pans weigh the same, they stay level. If you add 2 kg to the **left**, you must add 2 kg to the **right** — or the scale tips. ## Golden rule **Whatever you do to one side, do to the other side.** `x + 5 = 12` Subtract 5 from both sides: `x = 7` You may: - Add the same number to both sides - Subtract the same - Multiply both sides by the same (not zero) - Divide both sides by the same (not zero) > Never subtract 5 from only the left. That is cheating the scale. ## The golden rule, slowly Imagine a real market scale. Left pan = right pan. If you place a mango on the left, the left drops — unless you place an identical mango on the right. Algebra is that scale made of numbers. ### Allowed pair-moves - Add the same number to both sides - Subtract the same number from both sides - Multiply both sides by the same non-zero number - Divide both sides by the same non-zero number ### How to write it (copy this habit) ``` x + 5 = 12 x + 5 − 5 = 12 − 5 x = 7 ``` One action, both sides, new line. ### Why we bother Later, two-step and three-step equations are just this rule used twice or three times. If the rule is soft now, those lessons collapse.