1/2-what=-1 3/4

1/2-what=-1 3/4

$$\begin{array}{rcl}
\frac{1}{2} -x &=& -1 \frac{3}{4} \quad | \quad *(-1)\\\\
-\frac{1}{2}+x &=& 1 \frac{3}{4} \quad | \quad +\frac{1}{2}\\\\
x &=& 1 \frac{3}{4}+\frac{1}{2}\\\\
x &=& \frac{4*1+3}{4}+\frac{1*2}{2*2}\\\\
x &=& \frac{7}{4}+\frac{2}{4}\\\\
x &=& \frac{9}{4}\\\\
x &=& \frac{8+1}{4}\\\\
x &=& \frac{8}{4}+\frac{1}{4}\\\\
x &=& 2+\frac{1}{4}\\\\
x &=& 2\frac{1}{4}
\end{array}$$

Thanks Heureka for going back and collecting these ones.

There are more unanswered questions from today as well.

I guess this will be the norm as the forum gets better known.

We can only do our best.  Thanks very much for all your wonderful contributions.