Hello, I need help with my revision for algebra

This was the teachers message:

#2 - The only thing missing now is the "or equal to" that is on the symbol in the question.

#5 - Are you saying that there are only two prices that she can sell the scarves for, $5 or $20?

Revisions needed: #2, 5

This was the original question:

2. x^²- 8x + 12>0

5. Katie makes and sells scarves. Her monthly profit is given by P(s) = -s²+ 25s - 100, where "s" is the selling price. For what range of prices can Katie sell the scarves, in order to make a profit? (For what values of "s" will -s²+ 25s - 100 be greater than 0?)

This was my answer:

2.x28x+12>0. 2

Factoring

(x-2)(x-6)>0

If two terms are positive, they are greater than zero

(x-2)(x-6)>0x2>0andx6>0

x>2andx>6.

Two terms are greater than zero when they are negative:

(x2)(x6)<0x2<0andx6<0

x<2andx<6

The solution of this inequality is the unison of two solutions

(,2)(6,+) (x<2 or x>6)

5.P(s)=-s^2+25s-100>0

-s^2+25s-100>0

-s^2+20s+5s-100>0

-s(s-20)+5(s-20)>0

(-s+5)(s-20)>0 ;

Study each case:

Case 1: -s + 5 >0 and s-20 >0

Case 2: -s + 5 <0 and s-20 <0.

the interval of this solution from the inequality is(5,20)

Katie should sell her scarves either for 5 and 20 in order to make a profit.

please write it out as i cannot read handwriting