Answer
$1$ or $-\displaystyle \frac{2}{3}$
Work Step by Step
$\left[\begin{array}{lll}
\text{2 times the reciprocal of a number } & \rightarrow & 2\cdot\frac{1}{x}\\\\
\text{ is subtracted from... } & \rightarrow & ... - 2\cdot\frac{1}{x}\\\\
\text{... 3 times the number } & \rightarrow & 3x - 2\cdot\frac{1}{x}\\ \\
\text{... the difference is 1 } & \rightarrow & 3x - 2\cdot\frac{1}{x}=1
\end{array}\right]$
$3x - 2\displaystyle \cdot\frac{1}{x}=1\qquad.../\times x$
$3x^{2}-2=x$
$3x^{2}-x-2=0$
... Trying with synthetic division, we find:
$$ \begin{array}{rrrr}
1 & | & 3 & -1 & -2 & \\
& & & 3 & 2 & \\
& & -- & -- & -- & \\
& & 3 & 2 & 0 &
\end{array}$$
$0=(x-1)(3x+2)$
$x=1$ or $x=-\displaystyle \frac{2}{3}$
