Answer
$\left\{ b|b\gt -1 \right\}
\text{ or }
\left( -1,\infty \right)
$
Work Step by Step
Using the properties of inequality, the given inequality, $
4b+7\gt2-b
,$ is equivalent to
\begin{array}{l}\require{cancel}
4b+b\gt2-7
\\\\
5b\gt-5
\\\\
b\gt-\dfrac{5}{5}
\\\\
b\gt-1
.\end{array}
Hence, the solution is $
\left\{ b|b\gt -1 \right\}
\text{ or }
\left( -1,\infty \right)
.$
