Solve the inequality: (2x^2 - 3) / x < 10

[wheatwoman]

Can some one please help me:

(2x^2 - 3) / x < 10

This is what I have so far:

(2x^2 - 3) / x - 10 < 0
(2x^2 - 3) - 10x / x < 0
(2x^2 - 10x - 3) / x < 0

this is when I get confused.

Thanks in advance.

 

[stapel]

(2x^2 - 10x - 3) / x < 0

this is when I get confused.

Find the zeroes of the numerator (the x-intercepts) and the denominator (the vertical asymptotes). These x-values will split the number line into intervals. Check the sign of the rational expression on each of these intervals. :idea:

The intervals on which the expression is negative will comprise the solution.

Eliz.

 

[nycfunction]

Can some one please help me:

(2x^2 - 3) / x < 10

This is what I have so far:

(2x^2 - 3) / x - 10 < 0
(2x^2 - 3) - 10x / x < 0
(2x^2 - 10x - 3) / x < 0

this is when I get confused.

Thanks in advance.

Here are the steps for solving rational inequalities:

1-Rearrange the inequality so that only 0 remains on the right side.

2-Create one fraction on the left side, if needed.

3-Factor the numerator and denominator.

4-Set each factor in the numerator equal to 0 and solve.

5-Set each factor in the denominator equal to 0 and solve.

6-Choose test points to find solution intervals.

I hope this helps.

 

[kasie-tutor]

Dear wheatwoman,

Have you heard about a "sign chart" or something similar? Do a Google search using the four keywords: solving inequalities sign chart. This will get you closer to what you are looking for. If my tutee weren't going to be here any minute I'd try to draw you a picture with 100 words.

 

[wheatwoman]

Got it Thanks it was just a nasty answer :evil: