Đáp án:
`3|x-2|+|3x+1|`
`=|3x-6|+|3x+1|`
Ta có tính chất:`|P|>=P,|P|>=-P`
`=>{(|3x+1|>=3x+1),(|3x-6|>=6-3x):}`
`=>3|x-2|+|3x+2|>=3x+1+6-3x=7`
Dấu "=" xảy ra khi `{(3x+1>=0),(3x-6<=0):}`
`<=>{(x>=-1/3),(x<=2):}`
`<=>-1/3<=x<=2`
Vậy `GTN N_{3|x-2|+|3x+1|}=7<=>-1/3<=x<=2`