Đáp án+Giải thích các bước giải:
`a)|2x-5|+3x=12`
`=>|2x-5|=12-3x`
Vì `|2x-5|>=0`
`<=>12-3x>=0`
`<=>12>=3x`
`<=>x<=4`
`=>[(2x-5=12-3x),(2x-5=3x-12):}`
`=>[(5x=17),(x=7(KTM)):}`
`=>x=17/5(TM)`
Vậy `x=17/5.`
`b)|x+1|+|x+2|+|x+3|=4x`
Vì `|x+1|+|x+2|+|x+3|>=0`
`=>4x>=0=>x>+0`
`=>{(|x+1|=x+1),(|x+2|=x+2),(|x+3|=x+3):}`
`=>x+1+x+2+x+3=4x`
`=>3x+6=4x`
`=>x=6(TM)`
Vậy `x=6.`
`c)|x^2+|x+2||=x^2+3`
Vì `x^2>=0,|x+2|>=0`
`=>|x^2+|x+2||=x^2+|x+2|`
`=>x^2+|x+2|=x^2+3`
`=>|x+2|=3`
`=>[(x+2=3),(x+2=-3):}`
`=>[(x=1),(x=-5):}`
Vậy `x=1` hoặc `x=-5.`
`d)|x^2-3|=6`
`=>[(x^2-3=-6),(x^2-3=6):}`
`=>[(x^2=-3(\text{vô lý})),(x^2=9):}`
`=>[(x=3),(x=-3):}`
Vậy `x=3` hoặc `x=-3`.
