Step 1

Given:

\(\displaystyle{\frac{{{2}{x}+{7}}}{{{8}}}}+{x}-{2}={\frac{{{x}-{1}}}{{{2}}}}\)

It contains signs therefore it is an equation.

\(\displaystyle\Rightarrow{\frac{{{2}{x}+{7}}}{{{8}}}}+{x}-{2}={\frac{{{x}-{1}}}{{{2}}}}\)

multiply by 8 we get,

\(2x+7+8x−16=4(x−1)\)

\(10x−9=4x−4\)

\(6x=9−4\)

\(6x=5\)

\(\displaystyle{x}={\frac{{{5}}}{{{6}}}}\)

Step 2

Therefore,

\(\displaystyle{x}={\frac{{{5}}}{{{6}}}}\)