Question

Negative 1 divided by 3x is greater than 5

Answer 1

`-(1)/(15)<x<0`

Explanation:

`(-1)/(3x)> 5 \\\\\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides}\\\\(-1)/(3x)-5>5-5\\\\Simplify\\-(1)/(3x)-5>0\\\\\mathrm{Simplify}\:-(1)/(3x)-5:\quad (-1-15x)/(3x)\\\\(-1-15x)/(3x)>0\\\\\mathrm{Multiply\:both\:sides\:by\:}3\\(3\left(-1-15x\right))/(3x)>0*\:3\\\\Simplify\\\\(-1-15x)/(x)>0\\\\\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}(-1-15x)/(x)\\\\\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:>\:0\\\\`

`-(1)/(15)<x<0`