#### Answer

$x\ge-3$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
5-(6-4x)\ge2x-7
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Removing the grouping symbols and using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
5-6+4x\ge2x-7
\\\\
4x-2x\ge-7-5+6
\\\\
2x\ge-6
\\\\
x\ge-\dfrac{6}{2}
\\\\
x\ge-3
.\end{array}