Modulus Inequality Help: Solving |x/2 + 3| > 3-x^2 and |e^x/2 - 3| > 3-e^(2x)

AI Thread Summary
The discussion centers on solving the modulus inequalities |x/2 + 3| > 3 - x^2 and |e^x/2 - 3| > 3 - e^(2x). The first inequality was solved, but the connection to the second inequality was unclear to participants, leading to speculation about a possible typo in the question. One participant suggested substituting u = e^x, transforming the second inequality into a similar form, but found it unhelpful. Ultimately, the correct substitution proposed was u = -e^x, which provided a clearer path to the solution. The conversation highlights the challenges in linking the two inequalities effectively.
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Homework Statement


Solve | \frac{x}{2} +3 | > 3-x^2
Hence, solve | \frac{e^x}{2} -3 | > 3-e^{2x}


Homework Equations





The Attempt at a Solution



I've solved the first part. But I have no clue what is the link to the second part?! could there be just typo to the question?? I can't find any links...
 
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Let u=e^x

and it becomes

|\frac{u}{2} +3 | > 3-u^2
 
Didn't help.

Anyway I figured the solution already.

should be let u= - e^x
 

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