My initial reaction is to try to isolate Q by taking it over to 30 so the equation would be 90-0.8=30/Q

The idea behind what you did is good, but the execution is flawed because you performed an "illegal" operation. You can't divide just one term in an expression - it's an all or nothing package deal. Consider the following:

\(\displaystyle 2x = 8\)

If we wanted to know the value of

*x*, we could divide both sides by 2, yielding:

\(\displaystyle \frac{2x}{2} = \frac{8}{2} \implies x = 4\)

Now, consider a slight variant on that exercise:

\(\displaystyle 2x + 1 = 9\)

Let's proceed with the exact same type of operation you did in your post, and divide only the

*x* term by 2:

\(\displaystyle \frac{2x}{2} + 1 = \frac{9}{2} \implies x + 1 = \frac{9}{2} \implies x = \frac{7}{2}\)

We can then plug this back in to check our answer:

\(\displaystyle 2 \left(\frac{7}{2} \right) + 1 = 7 + 1 = 8 \neq 9\)

Oh dear, that's not right at all! But where did we go wrong? Recall what I said earlier about division. What we should have done is:

\(\displaystyle \frac{2x + 1}{2} = \frac{9}{2} \implies x + \frac{1}{2} = \frac{9}{2} \implies x = \frac{8}{2} = 4\)

Ah, much better, that worked exactly as we intended.