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If $minus 9 over 5 less than minus 3 t plus 1 less than minus 7 over 4 comma$ what is one possible value of $9 t minus 3 ?$

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Any value greater than $bold 21 over bold 4$ and less than $bold 27 over bold 5$

Recognizing the structure of this inequality provides one solution strategy. With this strategy, a student will look at the relationship between $minus 3 t plus 1$ and $9 t minus 3$ and recognize that the latter is −3 multiplied by the former.

Multiplying all parts of the inequality by −3 reverses the inequality signs, resulting in $27 over 5 greater than 9 t minus 3 greater than 21 over 4 comma$ or rather $21 over 4 less than 9 t minus 3 less than 27 over 5$ when written with increasing values from left to right. Any value greater than $21 over 4$ and less than $27 over 5$ is correct.