SOLUTION: How would I: Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set x/(x+1)

SOLUTION: How would I: Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set x/(x+1) > 6x ?

Question 818521: How would I: Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set
x/(x+1) > 6x ?
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Do as , then multiply left and right by x+1. Realize x+1 may be either positive, zero ; or less than zero so:

If then ;

If then ;

So work with those both. Also realize, . Also, before solving both inequalities, you do not yet know if they form an intersection or a union.
The x at -1 is a critical point, and when you solve each of the two main inequalities each of them is also a critical point, so the critical points help form your intervals on x. You check any value in every interval to see if the original given inequality is satisfied or not satisfied.

Can you continue with this guidance as described?
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