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Help Solve This Inequality?

+3 votes
1/(5x^2 - 2x - 7) < 5/13

Can someone show me the steps to do this please? I only ever get half of the answer right and I have no idea why!!

Thanks in advance ;)
asked Jan 11, 2013 in ALGEBRA 1 by rockstar Apprentice

2 Answers

+3 votes
1..   1/(5x^2 - 2x - 7) < 5/13

multiply each side by  5x^2 -2x -7

     1< (5/13 ) * (5x^2 -2x -7)

multiply each side by 13

13 < 5*(5x^2 -2x -7)

13< 25x^2 -10x - 35

subtract 13 from eachside

13 -13<25x^2 -10x - 35- 13

25x^2 - 10x - 48 >0

comparing  the above inequality with ax^2+bx +c>0

a =25 , b =- 10 ,c =-48

the qradratic equation formula (- b± sqrt( b^2 -4ac)/2a

                                     = 10 ± sqrt(10^2 -(4*25*-48)/50

                                     =10 ± sqrt(100 +4800)50

                                     =10± sqrt(4900)/50

                                     =(10 +70)/50 ,(10 -70)/50

                                    =8/5 ,-6/5

    x -8/5>0  ,x +6/5>0

  x > 8/5,  x< 6/5

the solution is  8/5 <x < 6/5
answered Jan 11, 2013 by krish Pupil
0 votes

The rational inequality is image

Rewrite as image

And simplify left side.

image

image

image

image

Multiply each side of inequality by negitive one and flip the symbol.

image

image

image

image

image

image

The inequality critical values at x  = 8/5, = -6/5

x  = -1 x  = 7/5

The set of solutions of the inequality is the union of the interval [-6/5, 8/5] and the interval

(-1, 7/5).

Solution x  < -6/5

x  > 8/5

-1 < < 7/5.

answered May 27, 2014 by david Expert
edited May 27, 2014 by david

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