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8 July, 12:53

How many integers x satisfy - 2 < 4 + 3x < 2?

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  1. 8 July, 16:12
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    First, let's solve the inequality:

    Subtracting 4 from all 3 terms, we get - 6 < 3x < - 2

    Solving - 6 - 2, and solving 3x < - 2 results in x < - 2/3.

    Ask: which integers satisfy x>-2? Answers: - 1, 0, 1, 2, ...

    Also ask: which integers satisfy x < - 2/3? Answers: - 5, - 4, - 3, - 2, - 1

    Notice that the only integer that is found in both sets of possibilities is - 1. So, only one integer x satisfies the given inequality.
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