\(a)\)\(\left(111-x\right)+7^2=149\)
\(\Leftrightarrow\)\(\left(111-x\right)+49=149\)
\(\Leftrightarrow\)\(\left(111-x\right)=149-49\)
\(\Leftrightarrow\)\(111-x=100\)
\(\Leftrightarrow\)\(x=111-100\)
\(\Leftrightarrow\)\(x=11\)
\(b)\)\(\left|x\right|+18=163+\left(-45\right)\)
\(\Leftrightarrow\)\(\left|x\right|+18=163-45\)
\(\Leftrightarrow\)\(\left|x\right|+18=118\)
\(\Leftrightarrow\)\(\left|x\right|=118-18\)
\(\Leftrightarrow\)\(\left|x\right|=100\)
\(\Leftrightarrow\)\(x=100\)
\(c)\)\(7^{x-4}\times6=2058\)
\(\Leftrightarrow\)\(7^{x-4}=2058\div6\)
\(\Leftrightarrow\)\(7^{x-4}=343\)
\(\Leftrightarrow\)\(7^{x-4}=7^3\)
\(\Leftrightarrow\)\(x-4=3\)
\(\Leftrightarrow\)\(x=3+4\)
\(\Leftrightarrow\)\(x=7\)