L4 · Preservation of Equality: The Balance Model

Learning goal

“I can keep an equation true by doing the same thing to both sides - like keeping a balance scale level - and use that idea to free the unknown.”

Balance model — picturing an equation as a balance scale: the two sides weigh the same, and the scale must stay level.

Preservation of equality — the rule that an equation stays true if the same operation is done to both sides. ("Preservation" means keeping something safe - here, keeping the equality safe.)

Side — one part of an equation: everything left of the equals sign is the left side; everything right of it is the right side.

Worked example

Picture the equation 6 + 4 = 10 as a balance scale. Left pan: 6 + 4. Right pan: 10. The scale is level - that is what the equals sign means. Step 1: Add 3 to the LEFT pan only. Now the left pan holds 9 + 4 = 13 and the right pan still holds 10. 13 is not equal to 10 - the scale tips and the equation is FALSE. Step 2: Start over. Add 3 to BOTH pans: 9 + 4 = 13. The scale is level again - the equation stayed true. Say it plainly: whatever you do to one side, you must do to the other. That is preservation of equality, and it is the only legal move with equations.

Check yourself — explain it

Why did adding 3 to the left pan only break the equation?

Paired problem — example still visible

Start with 8 + 5 = 13. Subtract 2 from both sides and write the new true equation -> 6 + 5 = 11

Faded completion — last step is yours

"Start: 9 + 6 = 15. Add 4 to both sides: 13 + 6 = ___" -> 19

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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