Question

Which of the following integers is in the solution set of │1 – 3x│ < 5 ?

I -1
II 1
III 2

Answer 1

`|1-3x| < 5\\\\x=-1\\\\|1-3\cdot(-1)| < 5\\\\|1+3| < 5\\\\|4| < 5\\\\4 < 5-the\ true`



`x=1\\\\|1-3\cdot1| < 5\\\\|1-3| < 5\\\\|-2| < 5\\\\2 < 5-the\ true`



`x=2\\\\|1-3\cdot2| < 5\\\\|1-6| < 5\\\\|-5| < 5\\\\5 < 5-the\ false`





`|1-3x| < 5\\\\1-3x < 5\ \wedge\ 1-3x > -5\\\\-3x < 5-1\ \wedge\ -3x > -5-1\\\\-3x < 4\ /:(-3)\ \wedge\ -3x > -6\ /:(-3)\\\\x > -(4)/(3)\ \wedge\ x < 2\\\\x\in(-(4)/(3);\ 2)\\\\I\ x=-1\in(-(4)/(3);\ 2)\\\\II\ x=1\in(-(4)/(3);\ 2)\\\\III\ x=2\\otin(-(4)/(3);\ 2)`