You are Here: Home >< Maths

# Inequalities Watch

Announcements
For example, (2x+3)(x-1)<0 is -3/2x<x<1 but how do you know it's one inequality and not -3/2<x and 1>x

And then (3x+1)(1-x)<0 why would it be two separate inequalities of x<-3 and x>1?

Also as a third example (3x-2)(2x-1)>or equal to 0 is x<or equal to 1/2 and x>or equal to 2/3
2. (Original post by Lucofthewoods)
For example, (2x+3)(x-1)<0 is -3/2x<x<1 but how do you know it's one inequality and not -3/2<x and 1>x

And then (3x+1)(1-x)<0 why would it be two separate inequalities of x<-3 and x>1?

Also as a third example (3x-2)(2x-1)>or equal to 0 is x<or equal to 1/2 and x>or equal to 2/3
It is very simple if you sketch a parabola with the corresponding roots, then just look for which domain the parabola satisfies the inequality. Do enough of these and you'll start recognising these without a sketch.
3. (Original post by Lucofthewoods)
For example, (2x+3)(x-1)<0 is -3/2x<x<1 but how do you know it's one inequality and not -3/2<x and 1>x

And then (3x+1)(1-x)<0 why would it be two separate inequalities of x<-3 and x>1?

Also as a third example (3x-2)(2x-1)>or equal to 0 is x<or equal to 1/2 and x>or equal to 2/3
For the first consider (2x+3)(x-1) = 0

We know that the solutions are x = -3/2 or x = 1 so draw a sketch of the graph.

Which part of the graph represents the inequality you want to solve?

I would always suggest drawing a sketch as it is then clear.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 10, 2016
Today on TSR

### What does it take to get into Oxbridge?

These personal statements cracked the code.

### Have I wasted my time at uni?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• 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

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