#### Answer

$x=6$

#### Work Step by Step

Subtract $x$ and subtract $1$ on both sides, and then combine like terms to obtain:
$8x-x=43-1\\\\7x=42$
Divide by 7 on both sides to obtain:
$x=\dfrac{42}{7}
\\x=6$
Check:
$\begin{array}{ccc}
&8(6)+1&=&6+43
\\&48+1 &= &49
\\&49&=&49\end{array}$