Answer
$x=-7$
Work Step by Step
Using the properties of equality, the value of the variable that satisfies the given equation, $
-6x+1=43
,$ is
\begin{array}{l}\require{cancel}
-6x=43-1
\\\\
-6x=42
\\\\
x=\dfrac{42}{-6}
\\\\
x=-7
.\end{array}