#### Answer

$\left( -\dfrac{7}{13}, \infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-9x+3\lt4x+10
,$ use the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-9x-4x\lt10-3
\\\\
-13x\lt7
.\end{array}
Dividing both sides by a negative number and consequently reversing the sign, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{-13x}{-13}\gt\dfrac{7}{-13}
\\\\
x\gt-\dfrac{7}{13}
.\end{array}
Hence, the solution set is the interval $
\left( -\dfrac{7}{13}, \infty \right)
.$