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Mathematics

Find the greatest integer which is such that if 7 is added to its double, the resulting number becomes greater than three times the integer.

Linear Inequations

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Answer

Let the greatest integer=xAccording to the condition,2x+7>3x2x3x>7x>7x<7Value of x which is greatest = 6\text{Let the greatest integer} = x \\[0.5em] \text{According to the condition}, \\[0.5em] 2x + 7 \gt 3x \\[0.5em] \Rightarrow 2x - 3x \gt - 7 \\[0.5em] \Rightarrow -x \gt - 7 \\[0.5em] \Rightarrow x \lt 7 \\[0.5em] \therefore \text{Value of x which is greatest = 6}

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