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If I am given the inequality $x+6>7>2x$ then can I do the following to find the range of x

since $x+6>7$ so $x>1$ and since $7>2x$ so $\frac{7}{2}$ $>x$

This means

  7/2  > x
         x > 1

so $\frac{7}{2}$ $>x>1$

Is this correct ? According to my book "The expression $x+6>7>2x$ alone is insufficient to find the range of x"


Here is the exact question from the book using the expression $$$x+6>7>2x$$ which is greater $x$ or $3$ ?

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Yes what you have got is correct. – Host-website-on-iPage Jul 11 '12 at 6:30
Could I know what book you're using? – Ink Jul 11 '12 at 6:48
up vote 3 down vote accepted

What you’ve done to solve the inequality is fine. However, it doesn’t suffice to answer the actual question. The inequality tells you only that $$1<x<\frac72\;;$$ that leaves open the possibility that $x=2$, say, in which case $x<3$, but it also leaves open the possibility that $x=\frac{13}4$, in which case $x>3$. Or $x$ could equal $3$.

The point is that the interval $\left(1,\frac72\right)$ contains both numbers less than $3$ and numbers greater than $3$, so the fact that $x$ is in this interval doesn’t tell you how $x$ compares with $3$.

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@Rajeshwar: And that changes my answer considerably. – Brian M. Scott Jul 11 '12 at 6:42
Thanks for clearing that up . I guess since the question didn't specify whether x was an integer or not changed the answer to "Not enough Info" – Rajeshwar Jul 11 '12 at 6:47
@Rajeshwar: There wouldn’t be enough information even if it had specified that $x$ was an integer: it might be less than $3$ or equal to $3$, so you still couldn’t be sure that $3$ was the larger number (though you could be sure that $x$ wasn’t). – Brian M. Scott Jul 11 '12 at 6:50
Thanks, I agree. – Rajeshwar Jul 11 '12 at 6:53

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