[Iridonia]

Hey.

I'm really struggling with this one. In regards to which steps I've taken to solve it on my own, I got nothing but some pathetic attempts to isolate [ S] or play around with the formula. I'm spectacularly bad at this type of chemistry. I've read up on it but I still don't get it.
I'll try to translate it to the best of my ability.

The link between the substrate concentration [ S] and the initial velocity V₀ is given by the following equation:

V₀ = V_max*[ S]/K_m+[ S]

Indicate the amount of [ S] (in relation to K_m) in which V₀ = 66,67% of the maximal velocity.

Thank you

[Borek]

From the sound of it yours is not a problem with chemistry, but with algebra.

Note: shorthand that you used to enter the formula is incorrect, as it suggests second [itex]\left[S\right][/itex] is not part of the denominator. Adding parentheses will make the notation unambiguous.

Start by multiplying both sides by [itex](K_m + \left[S\right])[/itex].

[Babcock_Hall]

@OP,

Borek made a good point about notation.  An alternative way to perform the algebra is to divide both sides by V_max.

[Borek]

An alternative way to perform the algebra is to divide both sides by V_max.

While it is definitely a necessary step it won't help in solving for [itex]\left[S\right][/itex], which is probably the most challenging part of the manipulation.

[Iridonia]

Please guys,
I know the rules say I have to try and solve the equation on my own first, step-by-step, and that you're not allowed to just give me the answer, and that you're not doing other people's homework for them.

This is not homework. I'm retaking an exam in university, that does not allow you to retake/repeat a course. I don't have a teacher available, nor a class. You're 100% on your own if you have to study for a reexam. I tried to reach out to the tutor I paid to help me last time (which was winter 2021), but he is unavailable for health reasons. I haven't had math since upper secondary school in 2019.
For some reason, enzyme kinetics are exceedingly difficult for me to grasp. I've tried reading and watching youtube. It's embarrasing, but I still don't get it. The exam is on june 22 and there's a lot of other things I need to study, which means I can't afford to spend an immense amount of time on a single area at the cost of studying everything else. I've already wasted too much time on this and getting nowhere. Sorry for the wall of text, but I'm getting a little desperate here.

I really, really need someone to show me how to solve the equation, step by step. From that I'll likely be able to derive from it what I need to solve similar questions (of which there are several). Please, will you make an exception for me?

[Babcock_Hall]

Why don't you try doing one step of algebra and showing us the result?  If it is correct, we will say so; if it is incorrect, we will point you in the right direction.

[Babcock_Hall]

@OP,

This problem is as much about algebra as it is about enzyme kinetics.  Can you write an equation that is equivalent to  V₀ = 66,67% of the maximal velocity?