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