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TwiddleLab / Math / Algebra in Motion

Letters on Both Sides

Lesson 3 of 12 · 7 min · Free, no account needed

What you will learn

  • With the letter on both sides, take the same amount of it from both sides until it's on one side only.
  • Most equations have one solution: the two lines cross once.
  • Same letters but different numbers: no solution (parallel lines). Exactly the same: every number works (the same line).

Start the lesson

How the lesson goes

  1. Ana and Ben again, but no graph. When do they have the same?

    Ana has 20 coins and saves 5 a week, Ben has 50 and saves 2. Each bag is w, the number of weeks. Tap a week to try it.

  2. Take the same off both pans.

    Drag a bag off one pan and a bag off the other into the bin, then the 10s. When only bags face weights, tap a bag to share.

  3. Ben changes his plan. Can they never be equal?

    Turn the dial: it sets how many coins Ben saves a week. Find the plan where the scale can never be level.

  4. Letters on both sides.

    When the letter is on both sides, take the same amount of it from both sides: 5w + 20 = 2w + 50 becomes 3w + 20 = 50.

    Then solve as before: w = 10. That is one solution, the week where the two lines cross.

    Same letters but different numbers, like 2w + 20 = 2w + 50, has no solution: the lines are parallel. If both sides are exactly the same, every number is a solution.

  5. Build a scale that never tips.

    The left pan is 2x + 6. Fill the right pan so the scale stays level, whatever a bag weighs. The bag weight keeps changing.

  6. Game: the sorting belt.

    Each card is a scale. Drag it into its bin before it rides off. Three misses and the belt stops.

  7. Two gyms. After how many visits do they cost the same?

    Gym A: $30 to join, then $5 a visit. Gym B: no joining fee, $10 a visit. Each bag is v, the number of visits. Set your guess and Check.

  8. Pip solved 7x + 3 = 4x + 15 and got x = 5. Find the slip.

    Tap the row where the scale tipped, then pick what that row should say.

  9. Your scale meets Ana and Ben's.

    Tap a value. Which scale stays level?

Previous lesson: Undo, Undo · Next lesson: Two Unknowns, Two Scales · Part of the course: Algebra in Motion

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