What values of 'x' will be the solution to the inequality #15x - 2/x > 1#?

1 Answer
May 14, 2016

Answer:

The answer is #x in (-1/3;0) uu (2/5;+oo)#

Explanation:

We start with the inequality #15x-2/x>1#

First step in solving such inequalities is to determine the domain. We can write that the domain is: #D=RR-{0}# (all real numbers different from zero).

Next step in solving such (in)equalities is to move all terms to the left side leaving zero on the right side:

#15x-2/x-1>0#

Now we should write all terms as fractions with comon denominator:

#(15x^2)/x-2/x-x/x>0#

#(15x^2-x-2)/x>0#

Now we have to find zeros of the numerator. To do this we have to calculate the determinant:

#Delta=1-4*15*(-2)=1+120=121#

#sqrt(Delta)=11#

#x_1=(1-11)/(2*15)=-10/30=-1/3#

#x_2=(1+11)/(2*15)=12/30=-2/5#

Now we have to sketch the function to find intervals where the values are greater than zero:

graph{x(x+1/3)(x-2/5) [-0.556, 0.556, -0.1, 0.1]}

From this graph we can clearly see the siolution:

#x in (-1/3;0) uu (2/5;+oo)#