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I have been tasked with solving the following inequality:

[itex]\frac{1}{x}[/itex] < 4

Attached to this thread is my attempted solution. As you can see I begin with simply solving the inequality for x, and I obtain the result x > [itex]\frac{1}{4}[/itex]

Next, I convert the equation into what I thought was the proper form for a hyperbola. I realize now I should have left the equation alone because it was already in proper form. However, I figure now that graphing at this point in my attempt may have not been the correct thing to do.

Next I find the roots for the inequality. I find these to be 0, and [itex]\frac{1}{4}[/itex].

Once the roots are found, I find the possible intervals for the inequality. The intervals I use are the following: x<0, 0<x<[itex]\frac{1}{4}[/itex], and x>[itex]\frac{1}{4}[/itex].

I then set these up on a chart in order to find which intervals solve the inequality. However, I must have either set this up wrong or am going about this the wrong way. Any tips or guidance on where to go from here would be greatly appreciated.

[itex]\frac{1}{x}[/itex] < 4

Attached to this thread is my attempted solution. As you can see I begin with simply solving the inequality for x, and I obtain the result x > [itex]\frac{1}{4}[/itex]

Next, I convert the equation into what I thought was the proper form for a hyperbola. I realize now I should have left the equation alone because it was already in proper form. However, I figure now that graphing at this point in my attempt may have not been the correct thing to do.

Next I find the roots for the inequality. I find these to be 0, and [itex]\frac{1}{4}[/itex].

Once the roots are found, I find the possible intervals for the inequality. The intervals I use are the following: x<0, 0<x<[itex]\frac{1}{4}[/itex], and x>[itex]\frac{1}{4}[/itex].

I then set these up on a chart in order to find which intervals solve the inequality. However, I must have either set this up wrong or am going about this the wrong way. Any tips or guidance on where to go from here would be greatly appreciated.