Tucker was asked to solve the equation 5x + 3 = 6x + 1. He did not know if his first step should be to add 5 negative x-tiles, or 1 negative unit tile, to both sides. What advice would you give Tucker to help him decide on his first step? Explain. Thank you in advance, and please show your work! :)

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  The order doesn't matter. Both can be done at once.

Step-by-step explanation:

The goal of the solution process is to get x by itself on one side of the equal sign, with a constant by itself on the other side of the equal sign. The sequence of steps used to accomplish that goal is largely irrelevant, if that goal is the end result of the steps used.

Adding -5x first:

  5x +3 -5x = 6x -5x +1

  3 = x +1

  3 -1 = x + 1 - 1  . . . . add -1 to both sides

  2 = x

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Adding -1 first:

  5x +3 -1 = 6x +1 -1

  5x +2 = 6x

  5x -5x +2 = 6x -5x  . . . . . add -5x to both sides

  2 = x

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Adding -1 and -5x together:

  5x +3 -5x -1 = 6x +1 -5x -1

  2 = x

As we've seen above, the second step is to add what wasn't added in the first step. If the first step is to cancel unwanted unit tiles and x tiles in one fell swoop, then no second step is required.