Please simplify and show the complete solution. Thank you so much! To be clear the first term is 5 over 7a - 3 plus 3 over a less than 5a? To be exact its in rational form.
in Other Math Topics by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

(5/7a)-3+3/a<5a. Multiply through by 7a: 5-21a+21<35a^2 assuming a>0.

35a^2+21a-26>0 has irrational roots one of which is negative, which reverses the inequality.

The positive root is 0.61261 approx, and the negative root is -1.21261.

To satisfy the inequality, a<-1.21261 or a>0.61261.

To appreciate this better, 35a^2+21a-26 is a parabola which cuts the a axis (horizontal) at the roots. It's U-shaped so the vertex is below the intersection points. This means the parabola equation is negative between the roots, so it's positive outside the roots. Therefore a<negative root and a>positive root satisfies the inequality.

It's possible the question is supposed to read differently. Parentheses help to make the intention clear. If the first term is 5/(7a-3) the result is a cubic which doesn't factorise and the solution is more complicated involving an irrational root.

Another interpretation: 5/(7a-3+(3/a))<5a; 5a/(7a^2-3a+3)<5a; 1/(7a^2-3a+3)<1; 1<7a^2-3a+3; 7a^2-3a+2>0. This has no real roots and is always positive for all a. So this interpretation is going nowhere!

by Top Rated User (660k points)

Related questions

1 answer
asked Jan 13, 2014 in Pre-Algebra Answers by bianca | 119 views
1 answer
asked Mar 25, 2013 in Algebra 1 Answers by anonymous | 188 views
4 answers
asked Aug 20, 2012 in Algebra 1 Answers by anonymous | 168 views
1 answer
asked Oct 17, 2013 in Algebra 1 Answers by anonymous | 326 views
1 answer
asked Aug 27, 2013 in Algebra 1 Answers by shazza Level 1 User (560 points) | 126 views
2 answers
asked Jun 29, 2013 in Algebra 1 Answers by anonymous | 290 views
2 answers
asked Jan 19, 2012 in Algebra 1 Answers by anonymous | 1.6k views
1 answer
asked Sep 25, 2013 in Algebra 1 Answers by sameel | 177 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
83,155 questions
87,984 answers
1,978 comments
4,883 users