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2-35.

DESIGNING A TIGHTROPE

In problem 2-31, you found multiple ways to combine lengths to get an acrobat to the end of the tightrope.

1. This time, you are given lengths of $2$, $5$, and $9$ feet. With your team, decide if the acrobat could cross a tightrope of length $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, or $10$ feet. For each length that you think is possible, write an expression to represent the acrobat’s movements. Remember that you can combine rope lengths going forward (in the positive direction) or backward (in the negative direction). For each length that you think is not possible, explain why it is not possible.

2. Could you combine lengths of $2$, $6$, and $8$ feet to cross a tightrope $15$ feet long? Explain why or why not.