Question about equations with fractions please!

[MathBlock]

Hi guys so i'm really confused about this..

From the picture i do not understand two things:
1. Why is it that i can subtract (3/4)s from each side and i cannot do the same for the last step which involves (11/4)s?
2. Why for the last step you multiply (-4/11) to even out the equation instead of the other way around which is (-11/4)?

Thank you!

 

[Dr.Peterson]

You subtract 3/4 s from each side to undo the addition of 3/4 s on the right. That's because 3/4 s - 3/4 s = 0.

Subtracting -11/4 would not undo the multiplication by -11/4. To undo multiplication, you divide. In the case of a fraction, division is the same as multiplying by the reciprocal: to divide by -11/4, you multiply by -4/11. That is, -4/11 * -11/4 = 1.

Now, you could do other things, but they would not accomplish the goal. If you added 11/4 to -11/4 s, the result would be 11/4 - 11/4 s, which is not s. And your goal is to get s by itself!

 

[MathBlock]

Wow It makes sense now, thank you!!