Question

54) |1-2/3x|<1

Can someone help me for this question pls? I really want to know how I can solve this!!!

Answer 1

`|a| < b\iff a < b\ \wedge\ a > -b\\\\|a| > b\iff a > b\ \vee\ a < -b`

`\left|1-(2)/(3)x\right| < 1\iff1-(2)/(3)x < 1\ \wedge\ 1-(2)/(3)x > -1\ \ \ |\text{subtract 1 from both sides}\\\\-(2)/(3)x < 0\ \vedge\ -(2)/(3)x > -2\ \ \ \ |\text{change the signs}\\\\(2)/(3)x > 0\ \wedge\ (2)/(3)x < 2\ \ \ \ |\text{multiply both sides by 3}\\\\2x > 0\ \wedge\ 2x < 6\ \ \ \ |\text{divide both sides by 2}\\\\x > 0\ \wedge\ x < 3\to0 < x < 3\to x\in(0,\ 3)`