Đáp án:
`text{Bài 1}`
`a, |5x- 4| = |x + 2|`
`⇔ 5x - 4 = x + 2` `text{hoặc}` `5x - 4 = -x - 2`
`⇔ 5x - x = 4 + 2` `text{hoặc}` `5x + x = 4 - 2`
`⇔ 4x = 6` `text{hoặc}` `6x = 2`
`⇔ x = 3/2` `text{hoặc}` `x = 1/3`
`text{Vậy}` `x ∈ {3/2;1/3}`
`b, |2x - 3| - |3x + 2| = 0`
`⇔ |2x - 3| = |3x + 2|`
`⇔ 2x - 3 = 3x + 2` `text{hoặc}` `2x - 3 = -3x - 2`
`⇔ 2x - 3x = 3 + 2` `text{hoặc}` `2x + 3x = 3 - 2`
`⇔ -x = 5` `text{hoặc}` `5x = 1`
`⇔ x = -5` `text{hoặc}` `x = 1/5`
`text{Vậy}` `x ∈ {-5;1/5}`
`c, |2 + 3x| = |4x - 3|`
`⇔ 2 + 3x = 4x - 3` `text{hoặc}` `2 + 3x = -4x + 3`
`⇔ 2 + 3 = 4x - 3x` `text{hoặc}` `2 - 3 = -4x - 3x`
`⇔x=5` `text{hoặc}` `x = 1/7`
`text{Vậy}` `x ∈ {5;1/7}`
`d, |7x + 1| - |5x + 6| = 0`
`⇔ |7x + 1| = |5x + 6|`
`⇔ 7x + 1 = 5x + 6` `text{hoặc}` `7x + 1 = -5x - 6`
`⇔ 7x - 5x = -1 + 6` `text{hoặc}` `7x + 5x = -1 - 6`
`⇔ 2x = 5` `text{hoặc}` `12x = -7`
`⇔ x = 5/2` `text{hoặc}` `x =(-7)/12`
`text{Vậy}` `x ∈ {5/2; (-7)/12}`
`text{Bài 2}`
`a, |3/2x + 1/2| = |4x - 1|`
`⇔ 3/2x + 1/2 = 4x - 1` `text{hoặc}` `3/2x + 1/2 = -4x + 1`
`⇔ 3/2x - 4x = -1/2 - 1` `text{hoặc}` `3/2x + 4x = -1/2 + 1`
`⇔ -5/2x =-3/2` `text{hoặc}` `11/2x = 1/2`
`⇔ x = 3/5` `text{hoặc}` `x = 1/11`
`text{Vậy}` `x ∈ {3/5; 1/11}`
`b, |5/4x - 7/2| - |5/8x + 3/5| = 0`
`⇔ |5/4x - 7/2| = |5/8x + 3/5|`
`⇔ 5/4x - 7/2 = 5/8x + 3/5` `text{hoặc}` `5/4x - 7/2 = -5/8x - 3/5`
`⇔ 5/4x - 5/8x = 7/2 + 3/5` `text{hoặc}` `5/4x + 5/8x = 7/2 - 3/5`
`⇔ 5/8x = 41/10` `text{hoặc}` `15/8x = 29/10`
`⇔ x = 164/25` `text{hoặc}` `x = 116/75`
`text{Vậy}` `x ∈ {164/25; 116/75}`
`c, |7/5x + 2/3| = |4/3x - 1/4|`
`⇔ 7/5x + 2/3 = 4/3x - 1/4` `text{hoặc}` `7/5x + 2/3 = -4/3x + 1/4`
`⇔ 7/5x - 4/3x = -2/3 - 1/4` `text{hoăc}` `7/5x + 4/3x = -2/3 + 1/4`
`⇔ 1/15x = -11/12` `text{hoặc}` `41/15x = -5/12`
`⇔ x = -55/4` `text{hoặc}` `x = -25/164`
`text{Vậy}` `x ∈ {-55/4, -25/164}`
`d, |7/8x + 5/6| - |1/2x + 5| = 0`
`⇔ |7/8x + 5/6| = |1/2x + 5|`
`⇔ 7/8x + 5/6 = 1/2x + 5` `text{hoặc}` `7/8x + 5/6 = -1/2x - 5`
`⇔7/8x - 1/2x = -5/6 + 5` `text{hoặc}` `7/8x + 1/2x = -5/6 - 5`
`⇔ 3/8x = 25/6` `text{hoặc}` `11/8x = -35/6`
`⇔ x = 100/9` `text{hoặc}` `x = -140/33`
`text{Vậy}` `x ∈ {100/9; -140/33}`
