Appendix A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A9: 46

$ x=-4,-\frac{2}{5}$

Given: $|\frac{2x-1}{x+1}|=3$ As we know that if|x|=a then $x=±a$ …(1) Solve the given inequality as follows: Apply equation(1), we have $\frac{2x-1}{x+1}=±3$ $2x-1=±3(x+1)$ $2x-1=3(x+1)$ This implies $2x-3x=3+1$ $x=-4$ or $2x-1=-3(x+1)$ This implies $2x+3x=-3+1$ or $5x=-2$ $x=-\frac{2}{5}$ Hence, the solution are $ x=-4,-\frac{2}{5}$