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    Hi Guys,
    there's this question that i got stuck at about solving an inequality. basically i've done the graph and everything in the question but when i solve the inequality on the paper, the answer is different that than the graph represents. i've attached you the question and also the graph and also how i've done on the paper which gives me different answer. any help would be much appreciated .
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    (Original post by Alen.m)
    Hi Guys,
    there's this question that i got stuck at about solving an inequality. basically i've done the graph and everything in the question but when i solve the inequality on the paper, the answer is different that than the graph represents. i've attached you the question and also the graph and also how i've done on the paper which gives me different answer. any help would be much appreciated .
    It is not the case that if you have (x-7)^2 \leq 24 that x-7 \leq \pm \sqrt{24}.

    Otherwise, I could say that 5^2 \leq 30 \Rightarrow 5 \leq \pm\sqrt{30}. Does that make sense? How can 5 be less than -sqrt(30)?

    Instead. Once you have something like (x-7)^2 \leq 24 you should re-arrange it to (x-7)^2 - 24 \leq 0.

    Then sketch the graph of (x-7)^2 - 24, marking the coordinates where it crosses the x-axis. Then, look at the regions where the quadratic lies under the x-axis, write down this region, in which case, that is your inequality solved.
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    (Original post by Zacken)
    It is not the case that if you have (x-7)^2 \leq 24 that x-7 \leq \pm \sqrt{24}.

    Otherwise, I could say that 5^2 \leq 30 \Rightarrow 5 \leq \pm\sqrt{30}. Does that make sense? How can 5 be less than -sqrt(30)?

    Instead. Once you have something like (x-7)^2 \leq 24 you should re-arrange it to (x-7)^2 - 24 \leq 0.

    Then sketch the graph of (x-7)^2 - 24, marking the coordinates where it crosses the x-axis. Then, look at the regions where the quadratic lies under the x-axis, write down this region, in which case, that is your inequality solved.
    so are you saying that the solution to any inequality of the form (x+q)^2 - p<0 is only possible using graphs?like there isn't anyway solving it on the paper or is it not necessary for AS
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    (Original post by Alen.m)
    so are you saying that the solution to any inequality of the form (x+q)^2 - p<0 is only possible using graphs?like there isn't anyway solving it on the paper or is it not necessary for AS
    Well, at AS, I highly recommend using graphs.

    Otherwise, once you're more familiar with inequalities you can split it into binary cases like x &gt; q and work with moduli, etc... but honestly, just work with the graphs.
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    (Original post by Alen.m)
    so are you saying that the solution to any inequality of the form (x+q)^2 - p<0 is only possible using graphs?like there isn't anyway solving it on the paper or is it not necessary for AS
    Solve equal to zero in order to get the points on the graph where the curve crosses the x-axis.

    Add the inequality afterwards in order to find the region for x: if f(x) > 0 then you want the region of the curve above the axis, if f(x) < 0 then you want the region underneath.

    You don't need to draw a graph but visualising it as one is the simplest solution.
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    Thanks guys
 
 
 
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