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IM 8.4.5 Lesson: Solving Any Linear Equation

Author:GeoGebra Classroom Activities, IM 6 – 8 Math

Solve each equation mentally.

Below are 4 cards, each with an equation.

  1. With your partner, select a card and choose who will take the first turn.
  2. During your turn, decide what the next move to solve the equation should be, explain your choice to your partner, and then write it down once you both agree. Switch roles for the next move. This continues until the equation is solved.
  3. Choose a second equation to solve in the same way, trading the card back and forth after each move.
For the last two equations, choose one and solve it. Show your work below. Then, trade with your partner you finish to check one another's work.

Tyler says he invented a number puzzle. He asks Clare to pick a number, and then asks her to do the following:

  • Triple the number
  • Subtract 7
  • Double the result
  • Subtract 22
  • Divide by 6
Clare says she now has a -3. Tyler says her original number must have been a 3. How did Tyler know that?

Explain or show your reasoning.

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