## Intermediate Algebra for College Students (7th Edition)

$1$ or $-\displaystyle \frac{2}{3}$
$\left[\begin{array}{lll} \text{2 times the reciprocal of a number } & \rightarrow & 2\cdot\frac{1}{x}\\\\ \text{ is subtracted from... } & \rightarrow & ... - 2\cdot\frac{1}{x}\\\\ \text{... 3 times the number } & \rightarrow & 3x - 2\cdot\frac{1}{x}\\ \\ \text{... the difference is 1 } & \rightarrow & 3x - 2\cdot\frac{1}{x}=1 \end{array}\right]$ $3x - 2\displaystyle \cdot\frac{1}{x}=1\qquad.../\times x$ $3x^{2}-2=x$ $3x^{2}-x-2=0$ ... 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 $x=-\displaystyle \frac{2}{3}$