Question

Solve inequality. |3n-2|-2<1

Answer 1

$\text{Hello there! :)}$

$\boxed{-1/3 < n < 5/3}$

$|3n - 2| - 2 < 1$

$\text{Begin simplifying by adding 2 to both sides:}$

$|3n - 2| < 3$

$\text{ Solve for the positive and negative solutions:}$

$3n - 2 < 3\\\\3n < 5\\\\n < 5/3$

$-(3n - 2) < 3\\\\\text{Switch sign when dividing by a negative:}\\\\3n - 2 > - 3\\\\3n > - 1\\\\n > -1/3$

$\text{Therefore, the solutions for the inequality are:}\\\\-1/3 < n < 5/3$