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When Lakeesha solved the equation from problem 7-54, she reasoned this way:  

Since groups of equals 3 groups of , then I know that each group of must equal .”

  1. Do you agree with her reasoning? Explain.

    Recall the Equation Mat from problem 7-54.
    Each group of corresponds to each group of .

    Shaded tile is plus 1.  Tile is negative 1.

    Equation Mat, with an equal sign in the center, with tiles as follows:  Left side, 3 rows of 1 positive, x, and 1 positive unit. Right side, 3 rows of 4 positive units.

    Each row across both sides of the equation mat are highlighted separately. Each row includes: left side, 1 positive x, and 1 unit. Right side, 4 positive units.

  2. How can the result of Lakeesha’s reasoning be written?

  3. Verify that your answer from problem 7-54 will make the equation you wrote in part (b) true.

    Substitute your answer from problem 7-54 into the equation above and see if the equation is true.