APPENDIX A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A9: 23

$-1 \leq x \lt \frac{1}{2}$ The solution set is $~~[-1, \frac{1}{2})$

$4x \lt 2x+1 \leq 3x+2$ $4x \lt 2x+1~~$ and $~~2x+1 \leq 3x+2$ Then: $4x \lt 2x+1$ $2x \lt 1$ $x \lt \frac{1}{2}$ and $2x+1 \leq 3x+2$ $-1 \leq x$ Solution: $-1 \leq x \lt \frac{1}{2}$ The solution set is $~~[-1, \frac{1}{2})$