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Question

Number of integral values of x satisfying the given inequality 1|5x+8|5 is/are

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Solution

Given that 1|5x+8|5

Using a|x|b where a,b>0
bxa or axb

Here we have,
1|5x+8|555x+81 or 15x+85

135x9 or 75x3

135x95 or 75x35

x[135,95][75,35]

The integral values of x in above interval are {2,1}.
Thus there are two integral values of x satisfies the given inequality.

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