The numbers that satisfies the statement, three times a number, increased by 1 , is between -5 and 10 are -1,0,1 and 2.
Let the number that satisfies the above statement be x.
Hence, according to the question,
-5 < 3x + 1 < 10
Subtracting 1 from the inequality, we get,
-5 -1 < 3x + 1 - 1 < 10 - 1
-6 < 3x + 0 < 9
-6 < 3x < 9
Dividing the inequality by 3 , we get,
-6/3 < 3x/3 < 9/3
-2 < x < 3
Hence, x can be -1 , 0 , 1 and 2.
Hence, there are four possibilities for the number x.
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