Let's note:
x=the grade to be taken on the final examination

We write the inequality modeling the problem: \(\displaystyle\frac{{{0.86}+{0.88}+{0.92}+{0.84}+{2}{x}}}{{6}}\Rightarrow{0.90}\)

We solve the inequality: \(\displaystyle\frac{{{3.5}+{2}{x}}}{{6}}\Rightarrow{0.90}\)

\(\displaystyle{3.5}+{2}{x}\Rightarrow{6}{\left({0.90}\right)}\)

\(\displaystyle{3.5}+{2}{x}\Rightarrow{5.4}\)

\(\displaystyle{3.5}+{2}{x}-{3.5}\Rightarrow{5.4}-{3.5}\)

\(\displaystyle{2}{x}\Rightarrow{1.9}\)

\(\displaystyle{x}\Rightarrow\frac{{1.9}}{{2}}\)

\(\displaystyle{x}\Rightarrow{0.95}\)

We write the inequality modeling the problem: \(\displaystyle\frac{{{0.86}+{0.88}+{0.92}+{0.84}+{2}{x}}}{{6}}\Rightarrow{0.90}\)

We solve the inequality: \(\displaystyle\frac{{{3.5}+{2}{x}}}{{6}}\Rightarrow{0.90}\)

\(\displaystyle{3.5}+{2}{x}\Rightarrow{6}{\left({0.90}\right)}\)

\(\displaystyle{3.5}+{2}{x}\Rightarrow{5.4}\)

\(\displaystyle{3.5}+{2}{x}-{3.5}\Rightarrow{5.4}-{3.5}\)

\(\displaystyle{2}{x}\Rightarrow{1.9}\)

\(\displaystyle{x}\Rightarrow\frac{{1.9}}{{2}}\)

\(\displaystyle{x}\Rightarrow{0.95}\)