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M:C:SPR:2

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SAT

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PSAT/NMSQT

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PSAT 10

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Heart of Algebra

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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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Correct Answer: 
No
Correct Answer: 
No
Correct Answer: 
No
Correct Answer: 
No

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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.

Question Difficulty: 
easy
Objective: 

Students must convert an existing compound inequality into a different format and find a value that satisfies all conditions.