Why is the solution of $|1+3x|<6x$ only $x>1/3$? After applying the properties of modulus, I get $-6x<1+3x<6x$. And after solving each inequality, I get $x>-1/9$ and $x>1/3$, but why is $x>-1/9$ rejected?
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3Both your inequalities have to hold, not just one of them. – almagest Jun 10 '16 at 17:15
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$$6x>|1+3x|\ge0\implies x>0$$
lab bhattacharjee
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Thank you so much for your reply! Do you mind explaining your answer to me? I just started self-studying this topic and I'm not quite familiar with it yet – javainstaller Jun 10 '16 at 17:16
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You need $x$ to be both bigger than $1/3$ and bigger than $-1/9$. But clearly anything bigger than $1/3$ is automatically bigger than $-1/9$ as $1/3>-1/9$. So you only keep that solution.
R_D
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