Answer
(a) linear
(b) not linear
(c) linear
Work Step by Step
(a) $\displaystyle \frac{x}{2}+2x=10$ is the same as $\displaystyle \frac{5}{2}x-10=0$, which is linear.
(b) $\displaystyle \frac{2}{x}-2x=1$ is not linear because it has the term $x^{-1}$ and linear equations can't have negative powers of $x$.
(c) $x+7=5-3x$ is the same as $4x+2=0$, which is linear.