Help

[Hielly]

Need help on 11(d)(f)


thanks

[TrueTears]

Best way is to sketch the graph and find the x values.

For d) you should get or

for f) try this:





again sketch graph.

[Hielly]

Best way is to sketch the graph and find the x values.

For d) you should get or

for f) try this:






again sketch graph.

so i did (3x-2)(x+1) greater than 0

so x=2/3 and x=-1

how do you know if its greater or less than? you can tell by drawing a graph and looking at it right?

[TrueTears]

A more algebraic way (albeit longer!) would be this:

for d)



Case 1:

and

and

The 'general' solution here is

Case 2:

and

and

The 'general' solution here is

Combine the 2 cases and you get or


Notice the use of "and" and "or" when splitting cases, it is crucial that you don't get mixed up with these 2 important words.

[TrueTears]

Best way is to sketch the graph and find the x values.

For d) you should get or

for f) try this:






again sketch graph.

so i did (3x-2)(x+1) greater than 0

so x=2/3 and x=-1

how do you know if its greater or less than? you can tell by drawing a graph and looking at it right?

I assume you are talking about d)

If so yes it is just the x intercepts. Then you must find the values of x for which the graph is strictly larger than 0. This is easily seen from the graph.

[Hielly]

A more algebraic way (albeit longer!) would be this:

for d)



Case 1:

and

and

The 'general' solution here is

Case 2:

and

and

The 'general' solution here is

Combine the 2 cases and you get or


Notice the use of "and" and "or" when splitting cases, it is crucial that you don't get mixed up with these 2 important words.

Interesting, thanks!

[cipherpol]

A more algebraic way (albeit longer!) would be this:

for d)



Case 1:

and

and

The 'general' solution here is

Case 2:

and

and

The 'general' solution here is

Combine the 2 cases and you get or


Notice the use of "and" and "or" when splitting cases, it is crucial that you don't get mixed up with these 2 important words.

This may be stupid, but from the two solutions for x, how do you pick out the general solution?

[samuch]

A more algebraic way (albeit longer!) would be this:

for d)



Case 1:

and

and

The 'general' solution here is

Case 2:

and

and

The 'general' solution here is

Combine the 2 cases and you get or


Notice the use of "and" and "or" when splitting cases, it is crucial that you don't get mixed up with these 2 important words.

This may be stupid, but from the two solutions for x, how do you pick out the general solution?

ill take a guess since with case 1 the signs being used at the start are 'greater than' zero then you pick the answer that is greater than zero and for case 2 since the sign at the start being used is the 'less than' zero sign then you pick the answer that is less than zero

Edit: remember that i may be completely wrong tho!

[cipherpol]

A more algebraic way (albeit longer!) would be this:

for d)



Case 1:

and

and

The 'general' solution here is

Case 2:

and

and

The 'general' solution here is

Combine the 2 cases and you get or


Notice the use of "and" and "or" when splitting cases, it is crucial that you don't get mixed up with these 2 important words.

This may be stupid, but from the two solutions for x, how do you pick out the general solution?

ill take a guess since with case 1 the signs being used at the start are 'greater than' zero then you pick the answer that is greater than zero and for case 2 since the sign at the start being used is the 'less than' zero sign then you pick the answer that is less than zero

Edit: remember that i may be completely wrong tho!

haha, I'll trust that you're correct. Thanks for the help!

[Ilovemathsmeth]

I always found it easier to graph the function. For part (f), I'd draw in the line y = -2. I'd find where the function equals -2. Then judging from the graph, you can decide where the function is greater than -2 and less than -2.

Same applies for f(x) > 0, find where it equals zero then from the graph you can easily tell where it is greater.

How do I write in that maths font? I really like it!

[Gloamglozer]

How do I write in that maths font? I really like it!

You'll need to learn LaTex.  It's like BB coding but google "LaTex" and you'll find some good resources.

[TrueTears]

A more algebraic way (albeit longer!) would be this:

for d)



Case 1:

and

and

The 'general' solution here is

Case 2:

and

and

The 'general' solution here is

Combine the 2 cases and you get or


Notice the use of "and" and "or" when splitting cases, it is crucial that you don't get mixed up with these 2 important words.

This may be stupid, but from the two solutions for x, how do you pick out the general solution?

For case 1, anything larger than 2/3 is larger than -1. so x>2/3 is more general

For case 2, apply same logic.

[TrueTears]

A more algebraic way (albeit longer!) would be this:

for d)



Case 1:

and

and

The 'general' solution here is

Case 2:

and

and

The 'general' solution here is

Combine the 2 cases and you get or


Notice the use of "and" and "or" when splitting cases, it is crucial that you don't get mixed up with these 2 important words.

This may be stupid, but from the two solutions for x, how do you pick out the general solution?

ill take a guess since with case 1 the signs being used at the start are 'greater than' zero then you pick the answer that is greater than zero and for case 2 since the sign at the start being used is the 'less than' zero sign then you pick the answer that is less than zero

Edit: remember that i may be completely wrong tho!

Close guess but no cigar

What if we had (x+1)(3x-2) < 0

Case 1

x+1<0 and 3x-2>0

x<-1 and x > 2/3

Here there is NO general solution. (So you wouldn't pick the x<-1)

Case 2

x+1>0 and 3x-2<0

x>-1 and x<2/3

Now this case has the actual solution: -1<x<2/3




This algebraic method is simply just to stimulate further thinking, graphing is the easiest way to go.

[samuch]

^ oh.. thanks for the correction