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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:



    What gives? >.<
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    Should be a combined inequality since it's less than/equal to zero
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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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    (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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    (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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    (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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    (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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