Rational Inequality: x / (x - 5) < 2 (check ans. please)

[chesterdg123]

Hi, I have received feedback that I have not finished the following rational inequality, any feedback will be appreciated. Thanks!

x/(x-5)<2

x/(x-5)-2=0

(x-5){x/(x-5)-2}=(x-5).0

x-2x+10=0

-x+10=0

-x=-10

x=10

The critical values are 5, and 10, They divide the x-axis into the intervals: (-00, 5), (5, 10), and (10, 00)

(-00, 5) f(4)=-6

(5, 10) f(6)=4

(10, 00) f(15)= -0.5

The function values are positive on (5, 10) and it is the solution set.

 

[skeeter]

Re: Rational Inequality

\(\displaystyle \frac{x}{x-5} < 2\)

\(\displaystyle \frac{x}{x-5} - 2 < 0\)

\(\displaystyle \frac{x}{x-5} - \frac{2(x-5)}{x-5} < 0\)

\(\displaystyle \frac{10-x}{x-5} < 0\)

critical values are at x = 5, and x = 10

the left side is negative for values of x such that x < 5 or x > 10, so there is your solution set.