The Balance Method

Algebra 1 · Axiom Academy

An equation is a balanced scale: whatever you do to one side, you must do to the other to keep it level. Think of an equation as a perfectly balanced scale. The left pan holds the unknown box x together with two unit weights; the right pan holds five unit weights. Because the scale hangs level , the two pans are equal in value — that is exactly what the equals sign means. 2. The Subtraction Property of Equality To get x by itself, we strip the two weights off the left pan. But removing them from the left alone would tip the scale. So we remove the same two weights from the right pan at the same moment — both sides drop by two, and the scale stays level. 3. The Addition Property of Equality The same rule runs in reverse for addition. Here x has had two weights taken away from it, shown as two empty slots that the box still "owes." We drop two real weights onto both pans: on the left they fill the slots and free the box; on the right they simply add on. Equal weight added to each side, so the scale stays level. 4. The Division Property of Equality What if the pan holds several boxes? Two identical boxes balance six weights. Since the boxes are equal and the weights split evenly, we can keep just half of each pan — one box on the left, three weights on the right. Halving both sides keeps the proportion, so the scale stays level and one box is revealed. 5. Putting It Together: A Two-Step Equation

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