Inequalities (1 Viewer)

[cutemouse]

Hey guys,

Just wondering, when you solve inequalities (eg. x²-4>0) do you prefer to use the case method, or to draw a facilitating graph and read off it?

What's the better method? I was taught the graphing method, so I'm wondering how you do the case method.

Thanks

 

[dp624]

I like to draw a very rough graph with only the x-axis, the x-intercepts and the general shape.
From there you can infer the answer. But i'm sure you know that

 

[PC]

For something like x²–4>0, a graph is probably sufficient.

For inequations like 1/(x²–4)>0 or 1/|x²–4|>0, definitely by cases.

 

[cutemouse]

1/(x²–4)>0

Why would I use cases for that?

Couldn't I just multiply both sides by (x²–4)² and then use a facilitating graph to read off it?

Oh, and with the 'case method' I was referring to the method that uses no graphs at all.

 

[addikaye03]

Why would I use cases for that?

Couldn't I just multiply both sides by (x²–4)² and then use a facilitating graph to read off it?

Oh, and with the 'case method' I was referring to the method that uses no graphs at all.

1/(x^2-4)>0
x^2-4<0
(x-2)(x+2)=0
therefore x=+-2
Then use cases.... i cbf, but basically x-axis, label each area A,B,C.. Test point e.g B (usually x=0, if possible) then rewrite equality.

 

[gurmies]

I use a different method, which I use for every inequality there is:

x^2 - 4 > 0

I solve as x^2 - 4 = 0

x = +- 2

Plot those two on a number line, then test outside and between for the inequality. Works for every type of inequality.

 

[jet]

for something like x^2-4>0
I would just solve x^2 -4 =0 then test between the two intercepts, namely -2 and 2. I would test x=0.
If it works then its in the interval. If not, then its outside.

Otherwise I'd draw a graph.

 

[bored of sc]

I use a different method, which I use for every inequality there is:
x^2 - 4 > 0
I solve as x^2 - 4 = 0
x = +- 2
Plot those two on a number line, then test outside and between for the inequality. Works for every type of inequality.

Same method we learnt.

 

[cutemouse]

Hmm, that's a bit different to the method that we learnt... Oh well I think my method's better.. Less mucking around.

 

[Trebla]

I usually use the graph method because it's quicker without the need to consider cases. The only time I would consider testing different cases is if there is a sum/difference of two or more absolute values in the inequality.

 

[cutemouse]

Yeah I use the case method aswell for multiple absolute values in an inequality. But I was wondering what was so good about the case method for doing this, as I've always used the graphing method. Looks like I'll stick with it.

 

[Aerath]

I usually use the graph method because it's quicker without the need to consider cases. The only time I would consider testing different cases is if there is a sum/difference of two or more absolute values in the inequality.

Yeah, that's the way I was taught it, too.

 

[Timothy.Siu]

lol,
i dont graph it, if its obvious like just a quadratic

 

[kurt.physics]

Graphing is probably quicker if its a quadratic, or even a cubic (required that the roots are easily found). Where as if it is hyperbolic or something weird, then multiplying by the square of the denominator, looking at the chases, or even equating the inequality will seem more appropriate.