The absolute value of \(\displaystyle-{\frac{{{9}}}{{{16}}}}{i}{s}\ {g}{r}{e}{a}{t}{e}{r}\ {t}{h}{a}{n}\ {t}{h}{e}\ {\left|{o}\right|}{l}{u}{t}{e}\ {v}{a}{l}{u}{e}\ {o}{f}-{\frac{{{3}}}{{{16}}}}\), so their sum must be negative.

Since \(-\frac{3}{4}\) is a positive number, it is not the correct solution.