# Inequalities help

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I'm doing a question with inequalities which i initially thought was very simple...

"solve the inequality ((2x-5)/(x+1))<1"

I solved it as if < is a = and eventually got x<6 (which is correct) but there were additional workings to find -1<x which i dont get where that has come from??

In the workings they made the inequality into a quadratic inequality, which i get

help appreciated thanks )

"solve the inequality ((2x-5)/(x+1))<1"

I solved it as if < is a = and eventually got x<6 (which is correct) but there were additional workings to find -1<x which i dont get where that has come from??

In the workings they made the inequality into a quadratic inequality, which i get

*how*they get there, but couldn't you just multiply by (x+1) and get a simple linear inequality?help appreciated thanks )

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(Original post by

I'm doing a question with inequalities which i initially thought was very simple...

"solve the inequality ((2x-5)/(x+1))<1"

I solved it as if < is a = and eventually got x<6 (which is correct) but there were additional workings to find -1<x which i dont get where that has come from??

In the workings they made the inequality into a quadratic inequality, which i get

help appreciated thanks )

**madz_08**)I'm doing a question with inequalities which i initially thought was very simple...

"solve the inequality ((2x-5)/(x+1))<1"

I solved it as if < is a = and eventually got x<6 (which is correct) but there were additional workings to find -1<x which i dont get where that has come from??

In the workings they made the inequality into a quadratic inequality, which i get

*how*they get there, but couldn't you just multiply by (x+1) and get a simple linear inequality?help appreciated thanks )

2) You can, but dont have to, use a quadratic, but you have to be careful with point 1)

Last edited by mqb2766; 2 months ago

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(Original post by

1) What did you assume when you multiplied through by (x+1)?

2) You can, but dont have to, use a quadratic, but you have to be careful with point 1)

**mqb2766**)1) What did you assume when you multiplied through by (x+1)?

2) You can, but dont have to, use a quadratic, but you have to be careful with point 1)

still struggling a bit with the logic behind the -1 tbh

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1) not too sure...? Whenever i've solved inequalities ive always just thought of it as a normal equation and then tackle the <0 or >0 at the end (i.e drawing a graph and putting the inequalities in last)

still struggling a bit with the logic behind the -1 tbh

**madz_08**)1) not too sure...? Whenever i've solved inequalities ive always just thought of it as a normal equation and then tackle the <0 or >0 at the end (i.e drawing a graph and putting the inequalities in last)

still struggling a bit with the logic behind the -1 tbh

1/x < 1

This has solutions

x>1

x<0

Just sketch it.

What happens when you multiply an inequality by a negative number?

Last edited by mqb2766; 2 months ago

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(Original post by

For the logic behind the -1 part, you could recognize the problem is roughly

1/x < 1

This has solutions

x>1

x<0

Just sketch it.

What happens when you multiply an inequality by a negative number?

**mqb2766**)For the logic behind the -1 part, you could recognize the problem is roughly

1/x < 1

This has solutions

x>1

x<0

Just sketch it.

What happens when you multiply an inequality by a negative number?

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#6

(Original post by

You have to flip the inequality and hence x>-1 im assuming?

**madz_08**)You have to flip the inequality and hence x>-1 im assuming?

Last edited by mqb2766; 2 months ago

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(Original post by

Don't assume. Youve found one solution by when x+1>0. What happens when x+1<0? Work it through.

**mqb2766**)Don't assume. Youve found one solution by when x+1>0. What happens when x+1<0? Work it through.

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#8

(Original post by

Ok, I've reworked the question a few times now and getting a hold of it thanks very much for the help!!

**madz_08**)Ok, I've reworked the question a few times now and getting a hold of it thanks very much for the help!!

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