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## 'Mind Your Ps and Qs' printed from http://nrich.maths.org/

Leo, Lily, Pippa and Lewis from Fakenham
College sent us this entertaining solution

We transferred the equations onto cards so we could move them about
easily. Good idea!

These are the ones we got to match, then we coloured them in and
added glitter.Glittery maths? Excellent
idea .

$ x< 0 \Leftrightarrow x\int^x_0 ydy < 0$

$x=0 \Rightarrow \int^x_0 \cos y dy =0$

$0< x< 1\Rightarrow \cos(x/2)> \sin(x/2) $

$x> 2\Rightarrow x^3> 1 $

$x> 4\Rightarrow 2\int^{x^2}_0ydy> x^2$

$x=-2\Rightarrow |x|> 1$

$x=1\Rightarrow x^2+x-2=0 $

We didn't manage to get four of < => , but were pleased we
got this :)

You should be pleased! This was good
logical thinking. These seven were all correct, but
there was a mistake in an eighth one you included: $x^2+4x+4 =0
\Rightarrow x> 1$. Can you see why?

The full solution that we obtained
was

$x^3> 1 \Leftrightarrow x> 1$

$2\int^{x^2}_0ydy> x^2 \Leftrightarrow |x|> 1$

$x=-2 \Leftrightarrow x^2+4x+4 =0$

$x=1\Rightarrow x^2+x-2=0$

$0< x< 1 \Rightarrow \cos(x/2)> \sin(x/2)$

$x> 4\Rightarrow x> 2$

$x< 0 \Leftrightarrow x\int^x_0 ydy < 0$

$x=0 \Rightarrow \int^x_0 \cos y dy =0$