Question

||3x-4|-5|>1 pls solve i need help with it i give 100 points

Answer 1

Answer:

${ \tt{ | |3x - 4| - 5 | > 1 }} \\ \\ { \tt{ |3x - 4| > 1 ±5}}$

• Either |3x - 4| > 1 + 5 or |3x - 4| > 1 - 5

${ \tt{ |3x - 4| > 6 \: \: or \: \: - 4}}$

→ for |3x - 4| > 6:

${ \tt{ |3x - 4| > 6}} \\ \\ { \tt{3x > 6±4}} \\ \\ { \boxed{ \tt{ \: x = \frac{10}{3} \: \: or \: \: \frac{2}{3} }}}$

→ for |3x - 4| > -4:

${ \tt{ |3x - 4| > - 4}} \\ \\ { \tt{3x > - 4±4}} \\ \\ { \boxed{ \tt{ \: x > 0 \: \: or \: \: - \frac{8}{3} }}}$