#### Answer

$x=-\dfrac{4}{9}$

#### Work Step by Step

Using the properties of equality, the value of the variable that satisfies the given expression, $
4x+7=3-5x
,$ is
\begin{array}{l}\require{cancel}
4x+5x=3-7
\\\\
9x=-4
\\\\
x=\dfrac{-4}{9}
\\\\
x=-\dfrac{4}{9}
.\end{array}