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quick fp2 inequalities question

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1. https://8dedc505ac3fba908c50836f5905...%20Edexcel.pdf

for q3 part b, how would I solve this?

I worked out the eq (x+5)(x+2) > 0 but is this wrong?

I'm confused as to what they expect me to do to solve it
2. Whenever you have inequalities questions with this one mark 'hence or otherwise' bit, I always find it best to do it graphically.

The inequality is saying: "when is the line x+4 greater than the reciprocal graph 2/|X+3|"

Note that the reciprocal graph is always positive (above the X-axis).

Sketching the graphs leads to X>-2.
3. (Original post by Katiee224)
https://8dedc505ac3fba908c50836f5905...%20Edexcel.pdf

for q3 part b, how would I solve this?

I worked out the eq (x+5)(x+2) > 0 but is this wrong?

I'm confused as to what they expect me to do to solve it
I'm not sure a sketch would be sufficient for this (as in I don't know).

We can note that |x+3| = x+3 if x >-3. So any solution to part a, is also a solution to part b, as long as x > -3.

Now suppose x < -3
Then part b becomes x+4 > -2/(x+3)
Whence (x+4)(x+3) < -2
Sign reverses as x+3 < 0
Then x^2+7x + 14 < 0
which has no solution.

Hence the only solutions are the overlap of the solutions to part a with x>-3, which gives x>-2.

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