college algebra--please help

solve the following inequality
70x-51<70/x

I get this--but I do not know how to write the final answer in a solution set

70x-51<70/x

70x^2/x - 51x /x - 70/x < 0

70x^2 - 51x - 70/x <0

(10x + 7) (7x - 10)/x <0

x=0
(10x + 7)= 0
(7x - 10)=0

Can you please help me to write the answer in a solution set???

asked by Heather
  1. when you get to this point:

    70x^2/x - 51x /x - 70/x < 0

    multiply by x to get

    70x^2 - 51x - 70 < 0 and note that x≠0
    since 1/x is not defined for x=0

    now you have

    (10x+7)(7x-10) < 0

    At this point you should have some idea what you are looking for. You know it is a parabola which opens upward, and crosses the x-axis at -7/10 and 10/7.

    So, the interval between the roots satisfies the original inequality:

    -7/10 < x < 10/7

    Algebraically, since

    (10x+7)(7x-10) < 0, either

    (10x+7) < 0 and (7x-10) > 0
    or
    (10x+7) > 0 and (7x-10) < 0

    solve those and you will find a solution set which agrees to the interval above.

    posted by Steve
  2. oops. because x cannot be 0, the final solution is

    (-7/10,0) U (0,10/7)

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-Calc

    I am having a great deal of difficulty with this problem. An open box is formed by cutting squares out of a piece of cardboard that is 16 ft by 19 ft and folding up the flaps. a. what size corner squares should be cut to yield a
  2. calculus

    f(x)=(2x-1)^2(x^2-9) find f'(x)=0 So first derivative: f'(x)=16x^3-6x^2-70x+36 0 = 16x^3-6x^2-70x+36 Ok.. I know I should factor it somewhere.. I just couldn't see where.. Thanks!
  3. Algebra

    During a hurricane evacuation from the east coast of Georgia, a family traveled 260 miles west. For part of the trip, they averaged 70 mph, but as congestion got bad, they had to slow to 20 mph. If the total time of travel was 9
  4. math

    need to calculate total purchase price I can afford for a home. monthly income $5875. .28 x $5875.=$1645.monthly mortgage 7.70 interest for 25years.placing 25% of my yearly income down. this is as far as I have gotten... 7.70x =
  5. algebra

    Solve: C(x)=70x-1000
  6. Math

    (x+20)(x-9)(x+10)>0 Please help? I'm stuck...need to find the solution set. so far I have x^3+21x^2-70x-1800>0 am I correct so far? What do I need to do next?
  7. college algebra

    use the given zero to find the remaining zeros of the function h(x)=x^4-15x^3+60x^2+70x-816 zero: 5-3i
  8. College Algebra

    49x^4 - 70x^3 + 21x^2. Facotor out, relative to the intergers, all factors common to all terms.
  9. algebra

    70x-1=10x-70
  10. Algebra

    Factor quadratic expressions: 2x^2 + 9x + 4 10x^2 + 70x + 100 Solve quadratic equations by factoring: 2x^2 + 9x + 4 = 0 Solve by taking square roots: (x - 5)^2 - 81 = 0

More Similar Questions