Tetration

75 = 300 - 50x      Move "-50x" to the left side (it turns into +50x):

50x +75 = 300       Move 75 over to the right side:

50x = 225       Divide both sides by 50:

x = 4.5

A  two dimentional circle doesn't have a 'volume' but an 'area'. Spheres have volumes:

$$V = \frac{4}{3}pi*r^3$$

a-(-b) = a + b

Pairs of minuses cancel out, thus:

If there's an odd number of minuses, it gets minus.

If there's an even number of minuses, it gets plus.

(x - y)/z = a    Multiply (*) both sides by z

x - y = az        Add (+) y to both sides:

x = az + y

$$52\frac{1}{2}min/one..hour$$

Turn the mixed numbers into an improper fraction using this formula (can you see why it's true?):

$$a\frac{b}{c}=\frac{ac+b}{c}$$

We get:

$$52\frac{1}{2}=\frac{52*2+1}{2}=\frac{105}{2}$$

So we have 105/2 min's. We know that there's 60 min's in an hour, so we get:

$$\frac{105}{2}/60 = \frac{105}{2*60}=\frac{105}{120}=\frac{105/15}{120/15}=\frac{7}{8}$$

And this sounds correct, since 52.5 min's ≈ an hour

If a value increases with 8% then it's value is multiplied by 1.08.

500 *1.08⁶ ≈ 793

ln(x) = 1

e^ln(x) = e¹   

x = e           Because e^ln(w) = w 

Order of operations:

1. Solve what's inside the paranthesis

2. Multiply (*) / divide (:)

3. Add (+) / subtract (-)

4p + 5 - 7p = -1

5 - 3p  = -1      EITHER: Use the formula: a - b = -(b - a)

3p - 5 = 1

3p = 6

p = 2

OR: 

5 - 3p  = -1    Move the five over to the right side:

- 3p = -6      Multiply (*) both sides with -1:

3p = 6        Divide both sides by two

p = 2

$$2\frac{1}{2}/6$$

The general method 

Turn the mixed numerals into an improper fraction using this formula (can you see why it's true):

$$a\frac{b}{c}=\frac{ac+b}{c}$$

We get:

$$2\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}$$

Thus the whole expression gets:

$$\frac{5}{2}/6=\frac{5}{2*6}=\frac{5}{12}$$

The efficient method

Realise that 2 1/2 =2.5

We get: 2.5/6 = 5/12

Thx, I try to find a good balance between efficient writing and holistic and pedagogic answers :) 

Indeed, I believe I learn some English and some math along the way.

I'm from Norway, you know :)