Appendix A - Numbers, Inequalities, and Absolute Values - A Exercises - Page A9: 49

a) $3\lt x \lt 5$ b) $5.9 \lt x \lt 6$

a) $$|x-4| \lt 1$$ $$-1\lt x-4 \lt 1$$ $$-1+4\lt x-4+4 \lt 1+4$$ $$3\lt x \lt 5$$ ------------------------------------------------------------------------ b) $$|x-6| \lt 0.1$$ $$-0.1 \lt x-6 \lt 0.1$$ $$-0.1+6 \lt x-6+6 \lt 0.1+6$$ $$5.9 \lt x \lt 6.1$$