By Ben Ayed M., El Mehdi K., Pacella F.

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**Extra resources for Blow-up and symmetry of sign changing solutions to some critical elliptic equations**

**Example text**

7. Solve the following equations. u u–1 2–u ------------ – 3 = -------------- + 8 = 1 – u (b) (a) (c) 3 4 6 1 5 2 1 ----------- + 1 = ----------- (f) ------------ + 2 = ------------ (e) (d) y–1 x+1 y–1 x+1 Solve the following equations for x. (a) (b) x–b = b–2 a( x – b) = b + a x x x --- – a = --- – b --- – a = b (d) (e) a b a 1 – ax 1 – bx b+x b–x (g) (h) --------------- + --------------- = 0 ------------ = -----------a b a–x a+x Solve for x. (a) 2x = 8 (b) 5x – 3 = 12 (c) (d) 3 – 2x --------------- = 2 7 (e) 2 5x 1 ------ + --- = --3 3 2 (f) (g) 5 ( x – 1 ) = 12 (h) (j) a–2 x = b (k) Solve the following equations.

Also, when we want to go back down, why is the first elevator to arrive always going up? Is this a real phenomenon or is it just a subjective result of our impatience for the elevator to arrive? Or is it another example of Murphy’s Law; whatever can go wrong will go wrong? 10 Theory of Knowledge – CHAPTER This is quite a complex question, but a simple explanation might run as follows: 1 If we are waiting near the bottom of a tall building, there are a small number of floors below us from which elevators that are going up might come and then pass our floor.

U u–1 2–u ------------ – 3 = -------------- + 8 = 1 – u (b) (a) (c) 3 4 6 1 5 2 1 ----------- + 1 = ----------- (f) ------------ + 2 = ------------ (e) (d) y–1 x+1 y–1 x+1 Solve the following equations for x. (a) (b) x–b = b–2 a( x – b) = b + a x x x --- – a = --- – b --- – a = b (d) (e) a b a 1 – ax 1 – bx b+x b–x (g) (h) --------------- + --------------- = 0 ------------ = -----------a b a–x a+x Solve for x. (a) 2x = 8 (b) 5x – 3 = 12 (c) (d) 3 – 2x --------------- = 2 7 (e) 2 5x 1 ------ + --- = --3 3 2 (f) (g) 5 ( x – 1 ) = 12 (h) (j) a–2 x = b (k) Solve the following equations.