a]
[tex]|x-5|=1\\\\x-5=1 \ \vee \ x-5=-1\\\\x=6 \ \vee \ x=4[/tex]
b]
[tex]|x-8|=9\\\\x-8=9 \ \vee \ x-8=-9\\\\x=17 \ \vee \ x=-1[/tex]
c]
[tex]|x+6|=4\\\\x+6=4 \ \vee \ x+6=-4\\\\x=-2 \ \vee \ x=-10[/tex]
d]
[tex]|x+9|=2\\\\x+9=2 \ \vee \ x+9=-2\\\\x=-7 \ \vee \ x=-11[/tex]
e]
[tex]|x-\frac{1}{3}|=\frac{1}{6}\\\\x-\frac{1}{3}=\frac{1}{6} \ \vee \ x-\frac{1}{3}=-\frac{1}{6}\\\\x=\frac{1}{6}+\frac{2}{6} \ \vee \ x=-\frac{1}{6}+\frac{2}{6}\\\\x=\frac{1}{2} \ \vee \ x=\frac{1}{6}[/tex]
f]
[tex]|x+\frac{1}{4}|=\frac{3}{8}\\\\x+\frac{1}{4}=\frac{3}{8} \ \vee \ x+\frac{1}{4}=-\frac{3}{8}\\\\x=\frac{3}{8}-\frac{2}{8} \ \vee \ x=-\frac{3}{8}-\frac{2}{8}\\\\x=\frac{1}{8} \ \vee \ x=-\frac{5}{8}[/tex]
g]
[tex]|7-x|=\frac{1}{2}\\\\7-x=\frac{1}{2} \ \vee \ 7-x=-\frac{1}{2}\\\\x=7-\frac{1}{2} \ \vee \ x=7+\frac{1}{2}\\\\x=6\frac{1}{2} \ \vee \ x=7\frac{1}{2}[/tex]
h]
[tex]|\frac{1}{3}+x|=\frac{2}{3}\\\\\frac{1}{3}+x=\frac{2}{3} \ \vee \ \frac{1}{3}+x=-\frac{2}{3}\\\\x=\frac{2}{3}-\frac{1}{3} \ \vee \ x=-\frac{2}{3}-\frac{1}{3}\\\\x=\frac{1}{3} \ \vee \ x=-1[/tex]
