Question

|3x-2|>4 what are the steps to solve for this

Answer 1

bearing in mind that an absolute value expression is in effect a piece-wise function with a ± versions.

`\bf |3x-2|>4\implies \begin{cases} +(3x-2)>4\\ -(3x-2)>4 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ +(3x-2)>4\implies 3x-2>4\implies 3x>6\implies x>\cfrac{6}{3}\implies \boxed{x>2} \\\\[-0.35em] ~\dotfill\\\\ -(3x-2)>4\implies 3x-2\stackrel{\stackrel{flip}{\downarrow} }{<}-4\implies 3x<-2\implies \boxed{x<-\cfrac{2}{3}}`