college algebraplease help
posted by Heather
solve the following inequality
70x51<70/x
I get thisbut I do not know how to write the final answer in a solution set
70x51<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???

Steve
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)(7x10) < 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 xaxis 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)(7x10) < 0, either
(10x+7) < 0 and (7x10) > 0
or
(10x+7) > 0 and (7x10) < 0
solve those and you will find a solution set which agrees to the interval above. 
Steve
oops. because x cannot be 0, the final solution is
(7/10,0) U (0,10/7)
Respond to this Question
Similar Questions

PreCalc
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 box … 
Math
(x+20)(x9)(x+10)>0 Please help? I'm stuck...need to find the solution set. so far I have x^3+21x^270x1800>0 am I correct so far? 
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 = 1645. … 
College Algebra
49x^4  70x^3 + 21x^2. Facotor out, relative to the intergers, all factors common to all terms. 
calculus
f(x)=(2x1)^2(x^29) find f'(x)=0 So first derivative: f'(x)=16x^36x^270x+36 0 = 16x^36x^270x+36 Ok.. I know I should factor it somewhere.. I just couldn't see where.. Thanks! 
college algebra
use the given zero to find the remaining zeros of the function h(x)=x^415x^3+60x^2+70x816 zero: 53i 
algebra
Solve: C(x)=70x1000 
algebra
70x1=10x70 
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 
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 hours, …