Answer:
[tex]{ \tt{ | |3x - 4| - 5 | > 1 }} \\ \\ { \tt{ |3x - 4| > 1 ±5}}[/tex]
• Either |3x - 4| > 1 + 5 or |3x - 4| > 1 - 5
[tex]{ \tt{ |3x - 4| > 6 \: \: or \: \: - 4}}[/tex]
→ for |3x - 4| > 6:
[tex]{ \tt{ |3x - 4| > 6}} \\ \\ { \tt{3x > 6±4}} \\ \\ { \boxed{ \tt{ \: x = \frac{10}{3} \: \: or \: \: \frac{2}{3} }}}[/tex]
→ for |3x - 4| > -4:
[tex]{ \tt{ |3x - 4| > - 4}} \\ \\ { \tt{3x > - 4±4}} \\ \\ { \boxed{ \tt{ \: x > 0 \: \: or \: \: - \frac{8}{3} }}}[/tex]
