SamKeene
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#1
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No idea why I'm getting this wrong.. but..

(2x+3)^2 \leq 81

4x^2 + 12x -72 \leq 0

x^2 + 3x -18 \leq 0

(x+6)(x-3) \leq 0

x \leq -6

x \leq 3

Yet when I put it into autograph I get this:

Image

What gives? >.<
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Jackasnacks
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Should be a combined inequality since it's less than/equal to zero
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SamKeene
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#3
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(Original post by Jackasnacks)
Should be a combined inequality since it's less than/equal to zero
So yeah I consulted my book and you're right, silly mistake... Is it correct that I have to interpret the type of symbol such as \leq from a geometrical look at f(x)? Cannot it be done purely algebraically?
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james22
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(Original post by SamKeene)
So yeah I consulted my book and you're right, silly mistake... Is it correct that I have to interpret the type of symbol such as \leq from a geometrical look at f(x)? Cannot it be done purely algebraically?
If you don't want to use the graph, consider the various cases that arise seperately. Here it would be x>=3, -6<=x<=3, x<=-6.
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Jackasnacks
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(Original post by SamKeene)
So yeah I consulted my book and you're right, silly mistake... Is it correct that I have to interpret the type of symbol such as \leq from a geometrical look at f(x)? Cannot it be done purely algebraically?
Well yes but a quick 3 second sketch of the graph shows whether it's above/below axis
It should then be clear whether it's two separate equalities or a combined one
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davros
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(Original post by SamKeene)
So yeah I consulted my book and you're right, silly mistake... Is it correct that I have to interpret the type of symbol such as \leq from a geometrical look at f(x)? Cannot it be done purely algebraically?
Yes - if you want a result that is negative then the brackets must have opposite signs.
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atsruser
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(Original post by SamKeene)
No idea why I'm getting this wrong.. but..

(2x+3)^2 \leq 81

4x^2 + 12x -72 \leq 0
A minor point: here you can write (2x+3)^2 \le 81 \Rightarrow -9 \le 2x+3 \le 9 directly, which removes the need for factorisation.
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