#### Answer

$a=\dfrac{3}{8}$

#### Work Step by Step

Using the properties of equality, the value of the variable that satisfies the given expression, $
a+7-2a=14+7a-10
,$ is
\begin{array}{l}\require{cancel}
a-2a-7a=14-10-7
\\\\
-8a=-3
\\\\
a=\dfrac{-3}{-8}
\\\\
a=\dfrac{3}{8}
.\end{array}