Turn on thread page Beta

Solving inequality watch


    (Original post by around)
    Or you can do what OP originally suggested (as none of those expressions are ever negative)
    The LHS is \frac{3x+1}{x-1} and when x=0 surely the expression is negative.

    Also if x=-0.2 the RHS is negative.

    you will get (7x+1)(x+1)(x-1)>0 finally,then,look
    (1).suppose 7x+1>0,get x>-1/7,then(x+1)(x-1)>0;get x>1 & x<-1
    the intersection of x>-1/7 and x>1 & x<-1 will be x>1
    (2).suppose 7x+1<0,get x<-1/7,then(x+1)(x-1)<0;get -1<x<1
    the intersection of x<-1/7 and -1<x<1 will be -1<x<-1/7
    Union (1)and(2) will be the answer -1<x<-1/7 & x>1

    this inequality will be more diffcult when replace > with >=

    (Original post by steve2005)
    The LHS is \frac{3x+1}{x-1} and when x=0 surely the expression is negative.

    Also if x=-0.2 the RHS is negative.
    Multiply by {x-1}^2 and {x+1}^2 ?
    I meant these.
    • PS Helper

    PS Helper
    (Original post by D-Day)
    Changing the sign only happens when dividing by a negative constant. Here you are multiplying by an expression.
    Not true. When you multiply through by variables you have to consider the cases when what you're multiplying by is negative. So, in this case, you'd have to consider cases where:
    1. x + 1 \ge 0 and x - 1 \ge 0, that is x \ge 1
    2. x + 1 \ge 0 and x - 1 &lt; 0, that is -1 \le x &lt; 1
    3. x + 1 &lt; 0 and x - 1 &lt; 0, that is x &lt; -1

    It makes no difference whether it's constant or not.
Submit reply
Turn on thread page Beta
Updated: August 8, 2009

University open days

  • University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Fri, 14 Dec '18
  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
Were you ever put in isolation at school?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way


Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.