Word problem in full: Penelope is playing a number game with her sister, June. Penelope is thinking of a number and wants June to guess it. Five more than three times her number is between -1 and 38. Write a compound inequality that shows the range of numbers that Penelope might be thinking of.

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Let the number be n, then -1<3n+5<38 or -1≤3n+5≤38 depending on what is meant by “between”. We’ll assume the former. 

-1<3n+5<38, subtract 5 throughout: -6<3n<33, divide through by 3: -2<n<11, shows the number to be in the range (-2,11) or possibly [-2,11].

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